single subject research example

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Neag School of Education

Educational Research Basics by Del Siegle

Single subject research.

“ Single subject research (also known as single case experiments) is popular in the fields of special education and counseling. This research design is useful when the researcher is attempting to change the behavior of an individual or a small group of individuals and wishes to document that change. Unlike true experiments where the researcher randomly assigns participants to a control and treatment group, in single subject research the participant serves as both the control and treatment group. The researcher uses line graphs to show the effects of a particular intervention or treatment. An important factor of single subject research is that only one variable is changed at a time. Single subject research designs are “weak when it comes to external validity….Studies involving single-subject designs that show a particular treatment to be effective in changing behavior must rely on replication–across individuals rather than groups–if such results are be found worthy of generalization” (Fraenkel & Wallen, 2006, p. 318).

Suppose a researcher wished to investigate the effect of praise on reducing disruptive behavior over many days. First she would need to establish a baseline of how frequently the disruptions occurred. She would measure how many disruptions occurred each day for several days. In the example below, the target student was disruptive seven times on the first day, six times on the second day, and seven times on the third day. Note how the sequence of time is depicted on the x-axis (horizontal axis) and the dependent variable (outcome variable) is depicted on the y-axis (vertical axis).

Once a baseline of behavior has been established (when a consistent pattern emerges with at least three data points), the intervention begins. The researcher continues to plot the frequency of behavior while implementing the intervention of praise.

In this example, we can see that the frequency of disruptions decreased once praise began. The design in this example is known as an A-B design. The baseline period is referred to as A and the intervention period is identified as B.

Another design is the A-B-A design. An A-B-A design (also known as a reversal design) involves discontinuing the intervention and returning to a nontreatment condition.

Sometimes an individual’s behavior is so severe that the researcher cannot wait to establish a baseline and must begin with an intervention. In this case, a B-A-B design is used. The intervention is implemented immediately (before establishing a baseline). This is followed by a measurement without the intervention and then a repeat of the intervention.

Multiple-Baseline Design

Sometimes, a researcher may be interested in addressing several issues for one student or a single issue for several students. In this case, a multiple-baseline design is used.

“In a multiple baseline across subjects design, the researcher introduces the intervention to different persons at different times. The significance of this is that if a behavior changes only after the intervention is presented, and this behavior change is seen successively in each subject’s data, the effects can more likely be credited to the intervention itself as opposed to other variables. Multiple-baseline designs do not require the intervention to be withdrawn. Instead, each subject’s own data are compared between intervention and nonintervention behaviors, resulting in each subject acting as his or her own control (Kazdin, 1982). An added benefit of this design, and all single-case designs, is the immediacy of the data. Instead of waiting until postintervention to take measures on the behavior, single-case research prescribes continuous data collection and visual monitoring of that data displayed graphically, allowing for immediate instructional decision-making. Students, therefore, do not linger in an intervention that is not working for them, making the graphic display of single-case research combined with differentiated instruction responsive to the needs of students.” (Geisler, Hessler, Gardner, & Lovelace, 2009)

Regardless of the research design, the line graphs used to illustrate the data contain a set of common elements.

Generally, in single subject research we count the number of times something occurs in a given time period and see if it occurs more or less often in that time period after implementing an intervention. For example, we might measure how many baskets someone makes while shooting for 2 minutes. We would repeat that at least three times to get our baseline. Next, we would test some intervention. We might play music while shooting, give encouragement while shooting, or video the person while shooting to see if our intervention influenced the number of shots made. After the 3 baseline measurements (3 sets of 2 minute shooting), we would measure several more times (sets of 2 minute shooting) after the intervention and plot the time points (number of baskets made in 2 minutes for each of the measured time points). This works well for behaviors that are distinct and can be counted.

Sometimes behaviors come and go over time (such as being off task in a classroom or not listening during a coaching session). The way we can record these is to select a period of time (say 5 minutes) and mark down every 10 seconds whether our participant is on task. We make a minimum of three sets of 5 minute observations for a baseline, implement an intervention, and then make more sets of 5 minute observations with the intervention in place. We use this method rather than counting how many times someone is off task because one could continually be off task and that would only be a count of 1 since the person was continually off task. Someone who might be off task twice for 15 second would be off task twice for a score of 2. However, the second person is certainly not off task twice as much as the first person. Therefore, recording whether the person is off task at 10-second intervals gives a more accurate picture. The person continually off task would have a score of 30 (off task at every second interval for 5 minutes) and the person off task twice for a short time would have a score of 2 (off task only during 2 of the 10 second interval measures.

I also have additional information about how to record single-subject research data .

I hope this helps you better understand single subject research.

I have created a PowerPoint on Single Subject Research , which also available below as a video.

I have also created instructions for creating single-subject research design graphs with Excel .

Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education (6th ed.). Boston, MA: McGraw Hill.

Geisler, J. L., Hessler, T., Gardner, R., III, & Lovelace, T. S. (2009). Differentiated writing interventions for high-achieving urban African American elementary students. Journal of Advanced Academics, 20, 214–247.

Del Siegle, Ph.D. University of Connecticut [email protected] www.delsiegle.info

Revised 02/02/2024

10.2 Single-Subject Research Designs

Learning objectives.

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.1, which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.1 represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

Figure 10.2 Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research

Figure 10.1 Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behavior. Specifically, the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy (Sidman, 1960) [1] . The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the reversal design , also called the ABA design . During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behavior of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

The study by Hall and his colleagues employed an ABAB reversal design. Figure 10.2 approximates the data for Robbie. The percentage of time he spent studying (the dependent variable) was low during the first baseline phase, increased during the first treatment phase until it leveled off, decreased during the second baseline phase, and again increased during the second treatment phase.

Figure 10.3 An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design

Figure 10.2 An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design

Why is the reversal—the removal of the treatment—considered to be necessary in this type of design? Why use an ABA design, for example, rather than a simpler AB design? Notice that an AB design is essentially an interrupted time-series design applied to an individual participant. Recall that one problem with that design is that if the dependent variable changes after the treatment is introduced, it is not always clear that the treatment was responsible for the change. It is possible that something else changed at around the same time and that this extraneous variable is responsible for the change in the dependent variable. But if the dependent variable changes with the introduction of the treatment and then changes back with the removal of the treatment (assuming that the treatment does not create a permanent effect), it is much clearer that the treatment (and removal of the treatment) is the cause. In other words, the reversal greatly increases the internal validity of the study.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a multiple-treatment reversal design , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behavior for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

In an alternating treatments design , two or more treatments are alternated relatively quickly on a regular schedule. For example, positive attention for studying could be used one day and mild punishment for not studying the next, and so on. Or one treatment could be implemented in the morning and another in the afternoon. The alternating treatments design can be a quick and effective way of comparing treatments, but only when the treatments are fast acting.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a child with an intellectual delay, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades. One solution to these problems is to use a multiple-baseline design , which is represented in Figure 10.3. There are three different types of multiple-baseline designs which we will now consider.

Multiple-Baseline Design Across Participants

In one version of the design, a baseline is established for each of several participants, and the treatment is then introduced for each one. In essence, each participant is tested in an AB design. The key to this design is that the treatment is introduced at a different time for each participant. The idea is that if the dependent variable changes when the treatment is introduced for one participant, it might be a coincidence. But if the dependent variable changes when the treatment is introduced for multiple participants—especially when the treatment is introduced at different times for the different participants—then it is unlikely to be a coincidence.

Figure 10.4 Results of a Generic Multiple-Baseline Study. The multiple baselines can be for different participants, dependent variables, or settings. The treatment is introduced at a different time on each baseline.

Figure 10.3 Results of a Generic Multiple-Baseline Study. The multiple baselines can be for different participants, dependent variables, or settings. The treatment is introduced at a different time on each baseline.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009) [2] . They were interested in how a school-wide bullying prevention program affected the bullying behavior of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviors they exhibited toward their peers. After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviors exhibited by each student dropped shortly after the program was implemented at his or her school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviors was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Multiple-Baseline Design Across Behaviors

In another version of the multiple-baseline design, multiple baselines are established for the same participant but for different dependent variables, and the treatment is introduced at a different time for each dependent variable. Imagine, for example, a study on the effect of setting clear goals on the productivity of an office worker who has two primary tasks: making sales calls and writing reports. Baselines for both tasks could be established. For example, the researcher could measure the number of sales calls made and reports written by the worker each week for several weeks. Then the goal-setting treatment could be introduced for one of these tasks, and at a later time the same treatment could be introduced for the other task. The logic is the same as before. If productivity increases on one task after the treatment is introduced, it is unclear whether the treatment caused the increase. But if productivity increases on both tasks after the treatment is introduced—especially when the treatment is introduced at two different times—then it seems much clearer that the treatment was responsible.

Multiple-Baseline Design Across Settings

In yet a third version of the multiple-baseline design, multiple baselines are established for the same participant but in different settings. For example, a baseline might be established for the amount of time a child spends reading during his free time at school and during his free time at home. Then a treatment such as positive attention might be introduced first at school and later at home. Again, if the dependent variable changes after the treatment is introduced in each setting, then this gives the researcher confidence that the treatment is, in fact, responsible for the change.

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, correlation coefficients, and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called visual inspection . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the level of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is trend , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behavior is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is latency , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

In the top panel of Figure 10.4, there are fairly obvious changes in the level and trend of the dependent variable from condition to condition. Furthermore, the latencies of these changes are short; the change happens immediately. This pattern of results strongly suggests that the treatment was responsible for the changes in the dependent variable. In the bottom panel of Figure 10.4, however, the changes in level are fairly small. And although there appears to be an increasing trend in the treatment condition, it looks as though it might be a continuation of a trend that had already begun during baseline. This pattern of results strongly suggests that the treatment was not responsible for any changes in the dependent variable—at least not to the extent that single-subject researchers typically hope to see.

Figure 10.5 Results of a Generic Single-Subject Study Illustrating Level, Trend, and Latency. Visual inspection of the data suggests an effective treatment in the top panel but an ineffective treatment in the bottom panel.

Figure 10.4 Results of a Generic Single-Subject Study Illustrating Level, Trend, and Latency. Visual inspection of the data suggests an effective treatment in the top panel but an ineffective treatment in the bottom panel.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001) [3] . (Note that averaging across participants is less common.) Another approach is to compute the percentage of non-overlapping data (PND) for each participant (Scruggs & Mastropieri, 2001) [4] . This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of non-overlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Key Takeaways

Single-subject research designs typically involve measuring the dependent variable repeatedly over time and changing conditions (e.g., from baseline to treatment) when the dependent variable has reached a steady state. This approach allows the researcher to see whether changes in the independent variable are causing changes in the dependent variable.
In a reversal design, the participant is tested in a baseline condition, then tested in a treatment condition, and then returned to baseline. If the dependent variable changes with the introduction of the treatment and then changes back with the return to baseline, this provides strong evidence of a treatment effect.
In a multiple-baseline design, baselines are established for different participants, different dependent variables, or different settings—and the treatment is introduced at a different time on each baseline. If the introduction of the treatment is followed by a change in the dependent variable on each baseline, this provides strong evidence of a treatment effect.
Single-subject researchers typically analyze their data by graphing them and making judgments about whether the independent variable is affecting the dependent variable based on level, trend, and latency.
Does positive attention from a parent increase a child’s tooth-brushing behavior?
Does self-testing while studying improve a student’s performance on weekly spelling tests?
Does regular exercise help relieve depression?
Practice: Create a graph that displays the hypothetical results for the study you designed in Exercise 1. Write a paragraph in which you describe what the results show. Be sure to comment on level, trend, and latency.
Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative. ↵
Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behavior support. Journal of Applied Behavior Analysis, 42 , 747–759. ↵
Fisch, G. S. (2001). Evaluating data from behavioral analysis: Visual inspection or statistical models. Behavioral Processes, 54 , 137–154. ↵
Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality, 9 , 227–244. ↵

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Single Subject Research

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Kurt A. Freeman 3 &
May Lim 3

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In this chapter, we describe basic and expert competencies for the use of single subject designs. Basic competencies include repeated observation of behavioral phenomenon of interest, the participant serving as his or her own control, and utilizing measurement and visual analysis strategies that allow one to determine whether change occurs over time. Expert competencies include basic competencies plus repeated demonstration of experimental effect and altering only one variable at a time when introducing treatment. Through the use of numerous examples, we illustrate how single subject research designs lend themselves well to various aspects of research, including the stage of theory development (Level 1 research) and more formal and systematic tests of said theories (Level II and Level III research). We also describe how basic and expert competencies of single subject designs can be incorporated into clinical practice to evaluate effects of intervention. The reader will learn how single subject designs are unique approaches to scientific inquiry due to several features, including repeated observation of the dependent variable(s), replication of treatment effects, intrasubject and intersubject comparisons, visual analysis of individual participant data, and systematic manipulation of independent variable(s). This chapter will likely be useful for clinicians and researchers alike who are interested in answering questions about clinical phenomena in a manner that meets the requirements of the scientific method.

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Behavioral Science Research Methods

Single-Case Designs

Anderson, C. M., Freeman, K. A., & Scotti, J. R. (1999). Evaluation of the generalizability (reliability and validity) of analog functional assessment methodology. Behavior Therapy, 30 , 21–30.

Article Google Scholar

Atkins, D. C., Bedics, J. D., McGlinchey, J. B., & Beauchaine, T. P. (2005). Assessing clinical significance: Does it matter which method we use? Journal of Consulting and Clinical Psychology, 73 , 982–989.

Article PubMed Google Scholar

Bailey, J. S., & Burch, M. R. (2002). Research methods in applied behavior analysis . Thousand Oaks, CA: Sage.

Google Scholar

Barlow, D., & Hersen, M. (1984). Single case experimental designs: Strategies for studying behavior change (2nd ed.). Elmsford, NY: Pergamon.

Blampied, N. M. (1999). A legacy neglected: Restating the case for single-case research in cognitive-behaviour therapy. Behaviour Change, 16 , 89–104.

Blampied, N. M. (2001). The third way: Single-case research, training, and practice in clinical psychology. Australian Psychologist, 36 , 157–163.

Campbell, D. T., & Stanley, J. C. (1966). Experimental and quasi-experimental designs for research and teaching . Chicago: Rand-McNally.

Chambless, D. L., & Hollon, S. D. (1998). Defining empirically supported therapies. Journal of Consulting and Clinical Psychology, 66 , 7–18.

Chambless, D. L., Sanderson, W. C., Shoham, V., Johnson, S. B., Pope, K. S., Crits-Christoph, P., et al. (1996). An update on empirically validated therapies. The Clinical Psychologist, 49 , 5–14.

Cook, D. J. (1996). Randomized trials in single subjects: The N of 1 study. Psychopharmacology Bulletin, 32 , 363–367.

PubMed Google Scholar

Freeman, K. A., & Piazza, C. C. (1998). Combining stimulus fading, reinforcement, and extinction to treat food refusal. Journal of Applied Behavior Analysis, 31 , 691–694.

Friman, P. C., Hoff, K. E., Schnoes, C., Freeman, K. A., Woods, D. W., & Blum, N. (1999). The bedtime pass: An approach to bedtime crying and leaving the room. Archives of Pediatric and Adolescent Medicine, 153 , 1027–1029.

Glicksohn, J., Gvirtsman, D., & Offer, S. (1997). The compensatory nature of mood: A single-subject time-series approach. Imagination, Cognition, & Personality, 15 , 385–396.

Harris, F. N., & Jenson, W. R. (1985a). Comparisons of multiple-baseline across persons designs and AB designs with replication: Issues and confusions. Behavioral Assessment, 7 , 121–127.

Harris, F. N., & Jenson, W. R. (1985b). AB designs with replication: A reply to Hayes. Behavioral Assessment, 7 , 133–135.

Hartmann, D. P., Roper, B. L., & Bradford, D. C. (1979). Some relationships between behavioral and traditional assessment. Journal of Behavioral Assessment, 1 , 3–21.

Hawkins, R. P., & Mathews, J. R. (1999). Frequent monitoring of clinical outcomes: Research and accountability for clinical practice. Education & Treatment of Children, 22 , 117–135.

Hayes, S. C. (1981). Single case experimental design and empirical clinical practice. Journal of Consulting and Clinical Psychology, 49 , 193–211.

Hayes, S. C. (1985). Natural multiple baselines across persons: A reply to Harris and Jenson. Behavioral Assessment, 7 , 129–132.

Hayes, S. C., Barlow, D. H., & Nelson-Gray, R. O. (1999). The scientist practitioner: Research and accountability in the age of managed care . Boston: Allyn and Bacon.

Hersen, M. (1982). Single-case experimental designs. In Bellack, A. S., & Hersen, M., Kazdin, A. E. (Eds.), International handbook of behavior modification and therapy (pp. 167–203). New York: Plenum Press.

Hilliard, R. B. (1993). Single-case methodology in psychotherapy process and outcome research. Journal of Consulting and Clinical Psychology, 61 , 373–380.

Holcombe, A., Wolery, M., & Gast, D. L. (1994). Comparative single-subject research: Descriptions of designs and discussions of problems. Topics in Early Childhood Special Education, 14 , 119–145.

Holttum, S., & Goble, L. (2006). Factors influencing levels of research activity in clinical psychologists: A new model. Clinical Psychology & Psychotherapy, 13 , 339–351.

Horner, R. H., Carr, E. G., Halle, J., McGee, G., Odom, S., & Wolery, S. (2005). The use of single-subject research to identify evidence-based practice in special education. Exceptional Children, 71 , 165–179.

Hrycaiko, D., & Martin, G. L. (1996). Applied research studies with single-subject designs: Why so few? Journal of Applied Sports Psychology, 8 , 183–199.

Jacobson, N. S., Roberts, L. J., Berns, S. B., & McClinchey, J. B. (1999). Methods for defining and determining the clinical significance of treatment effects: Description, application, and alternatives. Journal of Consulting and Clinical Psychology, 67 , 300–307.

Jacobson, N. S., & Truax, P. (1991). Clinical significance: A statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59 , 12–19.

Jones, E. E. (Ed.). (1993). Special section: Single-case research in psychotherapy. Journal of Consulting and Clinical Psychology , 61 , 371–430.

Kahng, S., Iwata, B. A., DeLeon, I. G., & Wallace, M. D. (2000). A comparison of procedures for programming noncontingent reinforcement schedules. Journal of Applied Behavior Analysis, 33 , 223–231.

Kazdin, A. E. (1999). Clinical significance: Measuring whether interventions make a difference. In Kazdin, A. E. (Ed.), Methodological issues & strategies in clinical research (3rd ed.). Washington, DC: American Psychological Association.

Kazdin, A. E. (2001). Behavior modification in applied settings (6th ed.). Belmont, CA: Wadsworth/Thomson Learning.

Kazdin, A. E. (2003). Research design in clinical psychology (4th ed.). Boston: Allyn and Bacon.

Kazdin, A. E., & Kopel, S. A. (1975). On resolving ambi-guities of the multiple-baseline design: Problems and recommendations. Behavior Therapy, 6 , 601–608.

Kazdin, A. E., & Weisz, J. R. (Eds.). (2003). Evidence-based psychotherapies for children and adolescents . New York: Guilford.

Krishef, C. H. (1991). Fundamental approaches to single subject design and analysis . Melbourne, FL: Robert E Krieger.

Leary, M. R. (2001). Introduction to behavioral research methods . Boston: Allyn and Bacon.

Lundervold, D. A., & Belwood, M. F. (2000). The best kept secret in counseling: Single-case ( N = 1) experimental designs. Journal of Counseling and Development, 78 , 92–102.

Mansell, J. (1982). Repeated direct replication of AB designs. Journal of Behavior Therapy and Experimental Psychiatry, 13 , 261.

Mash, E. J., & Barkley, R. A. (Eds.). (2006). Treatment of childhood disorders (3rd ed.). New York: Guilford.

Miltenberger, R. G. (2001). Behavior modification: Principles and procedures. Belmont, CA: Wadsworth/Thomson Learning.

Morgan, D. L., & Morgan, R. K. (2001). Single-participant research design: Bridging science to managed care. American Psychologist, 56 , 119–127.

Nugent, W. R. (1992). The affective impact of a clinical social worker’s interviewing style: A series of single-case experiments. Research on Social Work Practice, 2 , 6–27.

Parker, R. I., Brossart, D. F., Vannest, K. J., Long, J. R., Garcia De-Alba, R., Baugh, F. G., et al. (2005). Effect sizes in single case research: How large is large? School Psychology Review, 34 , 116–132.

Perone, M. (1991). Experimental design in the analysis of free-operant behavior. In Iversen, I. H., & Lattal, K. A. (Eds.), Experimental analysis of behavior, Part I (pp. 135–171). Amsterdam, Netherlands: Elsevier.

Perone, M. (1999). Statistical inference in behavior analysis: Experimental control is better. The Behavior Analyst, 22 , 109–116.

Phelps, R., Eisman, E. J., & Kohout, J. (1998). Psychological practice and managed care: Results of the CAPP practitioner survey. Professional psychology: Research and practice, 29 , 31–36.

Scruggs, T. E., & Mastropieri, M. A. (1998). Summarizing single-subject research: Issues and applications. Behavior Modification, 22 (3), 221–242.

Sidman, M. (1960). Tactics of scientific research . Boston: Authors Cooperative.

Skinner, B. F. (1974). About behaviorism . Oxford: Knopf.

Task Force on Promotion and Dissemination of Psychological Procedures. (1995). Training in and dissemination of empirically-validated treatments: Report and recommendations. The Clinical Psychologist, 48, 3–23.

Todman, J. B., & Dugard, P. (2001). Single-case and small-n experimental designs: A practical guide to randomization tests . Mahwah, NJ: Erlbaum.

Watson, P. J., & Workman, E. A. (1981). The non-concurrent multiple-baseline across-individuals design: An extension of the traditional multiple-baseline design. Journal of Behavior Therapy and Experimental Psychiatry, 12 , 257–259.

Zhan, S., & Ottenbacher, K. J. (2003). Single subject research designs for disability research. Disability and Rehabilitation, 23 , 1–8.

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Freeman, K.A., Lim, M. (2010). Single Subject Research. In: Thomas, J.C., Hersen, M. (eds) Handbook of Clinical Psychology Competencies. Springer, New York, NY. https://doi.org/10.1007/978-0-387-09757-2_15

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Chapter 10: Single-Subject Research

Single-Subject Research Designs

Learning Objectives

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.2, which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.2 represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

A subject was tested under condition A, then condition B, then under condition A again.

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behaviour. Specifically, the researcher waits until the participant’s behaviour in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy (Sidman, 1960) [1] . The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the reversal design , also called the ABA design . During the first phase, A, a baseline is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behaviour of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

The study by Hall and his colleagues was an ABAB reversal design. Figure 10.3 approximates the data for Robbie. The percentage of time he spent studying (the dependent variable) was low during the first baseline phase, increased during the first treatment phase until it leveled off, decreased during the second baseline phase, and again increased during the second treatment phase.

A graph showing the results of a study with an ABAB reversal design. Long description available.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a multiple-treatment reversal design , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behaviour for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a developmentally disabled child, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades.

One solution to these problems is to use a multiple-baseline design , which is represented in Figure 10.4. In one version of the design, a baseline is established for each of several participants, and the treatment is then introduced for each one. In essence, each participant is tested in an AB design. The key to this design is that the treatment is introduced at a different time for each participant. The idea is that if the dependent variable changes when the treatment is introduced for one participant, it might be a coincidence. But if the dependent variable changes when the treatment is introduced for multiple participants—especially when the treatment is introduced at different times for the different participants—then it is extremely unlikely to be a coincidence.

Three graphs depicting the results of a multiple-baseline study. Long description available.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009) [2] . They were interested in how a school-wide bullying prevention program affected the bullying behaviour of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviours they exhibited toward their peers. (The researchers used handheld computers to help record the data.) After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviours exhibited by each student dropped shortly after the program was implemented at his or her school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviours was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, Pearson’s r , and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called visual inspection . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the level of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is trend , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behaviour is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is latency , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

In the top panel of Figure 10.5, there are fairly obvious changes in the level and trend of the dependent variable from condition to condition. Furthermore, the latencies of these changes are short; the change happens immediately. This pattern of results strongly suggests that the treatment was responsible for the changes in the dependent variable. In the bottom panel of Figure 10.5, however, the changes in level are fairly small. And although there appears to be an increasing trend in the treatment condition, it looks as though it might be a continuation of a trend that had already begun during baseline. This pattern of results strongly suggests that the treatment was not responsible for any changes in the dependent variable—at least not to the extent that single-subject researchers typically hope to see.

Results of a single-subject study showing level, trend and latency. Long description available.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001) [3] . (Note that averaging across participants is less common.) Another approach is to compute the percentage of nonoverlapping data (PND) for each participant (Scruggs & Mastropieri, 2001) [4] . This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of nonoverlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Key Takeaways

Single-subject research designs typically involve measuring the dependent variable repeatedly over time and changing conditions (e.g., from baseline to treatment) when the dependent variable has reached a steady state. This approach allows the researcher to see whether changes in the independent variable are causing changes in the dependent variable.
In a reversal design, the participant is tested in a baseline condition, then tested in a treatment condition, and then returned to baseline. If the dependent variable changes with the introduction of the treatment and then changes back with the return to baseline, this provides strong evidence of a treatment effect.
In a multiple-baseline design, baselines are established for different participants, different dependent variables, or different settings—and the treatment is introduced at a different time on each baseline. If the introduction of the treatment is followed by a change in the dependent variable on each baseline, this provides strong evidence of a treatment effect.
Single-subject researchers typically analyze their data by graphing them and making judgments about whether the independent variable is affecting the dependent variable based on level, trend, and latency.
Does positive attention from a parent increase a child’s toothbrushing behaviour?
Does self-testing while studying improve a student’s performance on weekly spelling tests?
Does regular exercise help relieve depression?
Practice: Create a graph that displays the hypothetical results for the study you designed in Exercise 1. Write a paragraph in which you describe what the results show. Be sure to comment on level, trend, and latency.

Long Descriptions

Figure 10.3 long description: Line graph showing the results of a study with an ABAB reversal design. The dependent variable was low during first baseline phase; increased during the first treatment; decreased during the second baseline, but was still higher than during the first baseline; and was highest during the second treatment phase. [Return to Figure 10.3]

Figure 10.4 long description: Three line graphs showing the results of a generic multiple-baseline study, in which different baselines are established and treatment is introduced to participants at different times.

For Baseline 1, treatment is introduced one-quarter of the way into the study. The dependent variable ranges between 12 and 16 units during the baseline, but drops down to 10 units with treatment and mostly decreases until the end of the study, ranging between 4 and 10 units.

For Baseline 2, treatment is introduced halfway through the study. The dependent variable ranges between 10 and 15 units during the baseline, then has a sharp decrease to 7 units when treatment is introduced. However, the dependent variable increases to 12 units soon after the drop and ranges between 8 and 10 units until the end of the study.

For Baseline 3, treatment is introduced three-quarters of the way into the study. The dependent variable ranges between 12 and 16 units for the most part during the baseline, with one drop down to 10 units. When treatment is introduced, the dependent variable drops down to 10 units and then ranges between 8 and 9 units until the end of the study. [Return to Figure 10.4]

Figure 10.5 long description: Two graphs showing the results of a generic single-subject study with an ABA design. In the first graph, under condition A, level is high and the trend is increasing. Under condition B, level is much lower than under condition A and the trend is decreasing. Under condition A again, level is about as high as the first time and the trend is increasing. For each change, latency is short, suggesting that the treatment is the reason for the change.

In the second graph, under condition A, level is relatively low and the trend is increasing. Under condition B, level is a little higher than during condition A and the trend is increasing slightly. Under condition A again, level is a little lower than during condition B and the trend is decreasing slightly. It is difficult to determine the latency of these changes, since each change is rather minute, which suggests that the treatment is ineffective. [Return to Figure 10.5]

Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative. ↵
Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behaviour support. Journal of Applied Behaviour Analysis, 42 , 747–759. ↵
Fisch, G. S. (2001). Evaluating data from behavioural analysis: Visual inspection or statistical models. Behavioural Processes, 54 , 137–154. ↵
Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality, 9 , 227–244. ↵

The researcher waits until the participant’s behaviour in one condition becomes fairly consistent from observation to observation before changing conditions. This way, any change across conditions will be easy to detect.

A study method in which the researcher gathers data on a baseline state, introduces the treatment and continues observation until a steady state is reached, and finally removes the treatment and observes the participant until they return to a steady state.

The level of responding before any treatment is introduced and therefore acts as a kind of control condition.

A baseline phase is followed by separate phases in which different treatments are introduced.

Two or more treatments are alternated relatively quickly on a regular schedule.

A baseline is established for several participants and the treatment is then introduced to each participant at a different time.

The plotting of individual participants’ data, examining the data, and making judgements about whether and to what extent the independent variable had an effect on the dependent variable.

Whether the data is higher or lower based on a visual inspection of the data; a change in the level implies the treatment introduced had an effect.

The gradual increases or decreases in the dependent variable across observations.

The time it takes for the dependent variable to begin changing after a change in conditions.

The percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition.

Research Methods in Psychology - 2nd Canadian Edition Copyright © 2015 by Paul C. Price, Rajiv Jhangiani, & I-Chant A. Chiang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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The benefits of single-subject research designs and multi-methodological approaches for neuroscience research

1. introduction.

The scientific method is neither singular nor fixed; it is an evolving, plural set of processes. It develops and improves through time as methodology rises to meet new challenges (Lakatos, 1978 ; Hull, 1988 ; Kuhn and Hacking, 2012 ). “It would be wrong to assume that one must stay with a research programme until it has exhausted all its heuristic power, that one must not introduce a rival programme before everybody agrees that the point of degeneration has probably been reached” (Lakatos, 1978 ). These insights apply not least to experimental design approaches.

For better and for worse, no experimental design comes without limitation. We must accept that the realities of the world cannot be simplistically verified against universal standard procedures; we are free instead to explore how the progressive evolution of experimental design enables new advancement. This paper proposes support for a shift of focus in the methodology of experimental research in neuroscience toward an increased utilization of single-subject experimental designs. I will highlight several supports for this suggestion. Most importantly, single-subject methods can complement group methodologies in two ways: by addressing important points of internal validity and by enabling the inductive process characteristic of quality early research. The power of these approaches has already been somewhat established by key historical neuroscience experiments. Additionally, the individuated nature of subject matter in behavioral neuroscience makes the single-subject approach particularly powerful, and single-subject phases in a research program can decrease time and resource costs in relation to scientific gains.

2. Complimentary research designs

Though the completely randomized group design is considered by many to be the gold standard of evidence (Meldrum, 2000 ), its limitations as well as ethical and logistical execution difficulties have been noted: e.g., blindness to group heterogeneity, problematic application to individual cases, and experimental weakness in the context of other often-neglected aspects of study design such as group size, randomization, and bias (Kravitz et al., 2004 ; Grossman and Mackenzie, 2005 ; Williams, 2010 ; Button et al., 2013 ). Thus, the concept of a “gold standard” results not from the uniform superiority of a method, but from an implicit valuing of its relative strengths compared to other designs, all things being equal (even though such things as context, randomization, group size, bias, heterogeneity, etc. are rarely equal). There is an alternative to this approach. Utilizing a wider array of methods across studies can help compensate for the limitations of each and provide flexibility in the face of unequal contexts. In a multi-methodological approach, different experimental designs can be evaluated in terms of complementarity rather than absolute strength. If one experimental design is limited in a particular way, adding another approach that is stronger in that aspect (but perhaps limited in another) can provide a more complete picture. This tactic also implicitly acknowledges that scientific rigor does not proceed only from the single study; replication, systematic replication, and convergent evidence may proceed from a progression of methods.

I suggest adding greater utilization of single-subject design to the already traditionally utilized between-subject and within-subject group designs in neuroscience to achieve this complementarity. The advantages and limitations of these designs are somewhat symmetrical. Overall, single-subject experiments carry with them more finely-focused internal validity because the same subject (together with their array of individual characteristics) serves in both the experimental and control conditions. Unlike in typical within-subject group comparisons, the repetition of comparisons in single-subject designs control for other confounding variables, rendering n = 1 into a true experiment. While an unreplicated single-subject experiment by itself cannot establish external validity, systematic replication of single-subject experiments over the relevant range of individual differences can. On the other hand, group designs cannot demonstrate an effect on an individual level, but within-individual group studies can characterize the generality of effects across large populations in a single properly sampled study, and may be particularly suited to analyzing combined effects of multiple variables (Kazdin, 1981 ). Single subject and group approaches can also be hybridized to fit a study's goals (Kazdin, 2011 ). In the following sections, I will describe aspects of each approach that illustrate how the addition of single-subject methodology to neuroscience could be of use. I do not mean to exhaustively describe either methodology, which would be outside the scope of this paper.

2.1. Group designs

Group experimental designs 1 interrogate the effect of an independent variable (IV) by applying that variable to a group of people, other organisms, or other biological units (e.g., neurons) and usually—but not always—comparing an aggregated population measure to that of one or more control groups. These designs require data from multiple individuals (people, animals, cells, etc.). Group experiments with between-group comparisons often assign these individuals to conditions (experimental or control) randomly. Other group experiments (such as a randomized block design) assign individuals to conditions systematically to explicitly balance the groups according to particular pre-considered individual factors. In both cases, the assumption is that if alternative variables influence the dependent variable (DV), they are unlikely to do so differentially across groups. Group experiments with within-subject comparisons expose each individual to both experimental and control conditions at different times and compare the grouped measures between conditions; this approach assures that the groups are truly identical since the same individuals are included in both conditions.

Because they involve multiple individuals, some group designs can provide important information about the generality of an effect across the included population, especially in the case of within-subject group designs. Unfortunately, some often-misused aspects of group designs tend to temper this advantage. For example, restricted inclusion criteria are often necessary to produce clear results. When desired generality involves only such a restricted population (e.g., only acute stroke patients, or only layer IV glutamatergic cortical neurons), this practice carries no disadvantage. However, if the study aims to identify more widely applicable processes, stringent inclusion criteria can produce cleaner but overly conditional results, limiting external validity (Henrich et al., 2010 ). Further, the analysis approach taken in many group designs that narrowly examines changes in central tendency (such as the mean) of groups can limit the assessment of generality within the sampled population since averaging will wash out heterogeneity of effects. Other aspects of rigor in group designs can also affect external validity (e.g., Kravitz et al., 2004 ; Grossman and Mackenzie, 2005 ; Williams, 2010 ; Button et al., 2013 ).

Another limitation of group design logic is the practical difficulty of balancing individual differences between groups. In the case of between-group comparisons, these difficulties arise from selection bias, mortality, etc. Even well controlled studies can still produce probabilistically imbalanced groups, especially in the small sample sizes often used in neuroscience research (Button et al., 2013 ). Deliberately balanced groups or post-hoc statistical control may help, but the former introduces a potential problem with true randomization, and the latter is weaker than true experimental control. Within-subject group comparisons implement both experimental and control conditions for each individual in a group and therefore better control for individual differences, however these designs still do not experimentally establish effects within the individual since single manipulations of experimental conditions can be confounded with other changes on an individual level.

The typical focus on parameters such as the mean in the analysis of group designs can also threaten internal as well as external validity, particularly if the experimental question concerns biological or behavioral variables that are highly individually contextualized or developmentally variant. 2 This problem extends from the fact that aggregate measures across populations do not necessarily reflect any of the underlying individuals (e.g., Williams, 2010 ); for example, average brain functional mapping tends not to apply to individual brains (Brett et al., 2002 ; Dworetsky et al., 2021 ; Fedorenko, 2021 ; Hanson, 2022 ). This kind of problem is particularly amplified in the study of human behavior and brain sciences, which both tend to be highly idiosyncratic. In these cases, aggregated measures can mask key heterogeneity including contradictory effects of IVs. This can complicate the application of results to individuals: an issue especially relevant in clinical research (Sidman, 1960 ; Williams, 2010 ). Relatedly, the estimation of population-based effect size provides scant information with which to estimate effects and relevance for an individual. Post-hoc statistical analysis may help to tease out these issues, but verification still requires new experimentation. True generality of a scientific insight requires not only that effects occur with reasonable replicability across individuals, but that a reasonable range of conditions that would alter the effect can be predicted: a difficult point to discern in group studies. Thus, while group designs carry advantages insofar as they can be used to characterize effects across a whole population in a single experiment, those advantages can be and often are subverted. Perhaps counter-intuitively, single-subject approaches can be ideal for methodically discovering the common processes that underlie diversity within a population, which have made it particularly powerful in producing generalizable results (see next section).

2.2. Single-subject designs

Single-subject designs compare experimental to control conditions repeatedly over time within the same individual. Like group designs with within-subject comparisons, single-subject designs can control for individual differences, which remain constant. However, single-subject designs take individual control to a new level. Since other confounding changes may coincide with a single change in the IV, single-subject designs also require multiple implementations of the same manipulation so that the comparison can be repeated within the individual, controlling for the coincidental confounds of a single condition change. Additionally, single-subject designs measure multiple data points through time within each condition before any experimental change occurs to assess pre-existing variation and trends in comparisons with the subsequent condition. Of course, a single-subject experiment without inter-individual replication has no generality—systematic replications across relevant individual characteristics and contexts are generally required to establish external validity. However, the typical group design also often requires similar replication to establish the same validity, and unlike group designs single-subject studies are also capable of rigorously interrogating even the rarest of effects.

Because single-subject experiments deal well with individual effects, they are often used in clinical and closely applied disciplines, e.g., education (Alnahdi, 2015 ), rehabilitation and therapy (Tankersley et al., 2006 ), speech and language (Byiers et al., 2012 ), implementation science (Miller et al., 2020 ), neuropsychology (Perdices and Tate, 2009 ), biomedicine (Janosky et al., 2009 ), and behavior analysis (Perone, 1991 ). However, the single-subject design is not limited to clinical applications or to the study of rare effects; it can also be used for the study of generalizable individual processes via systematic replication. Serial replications often enable detailed distillation of both common and uncommon relevant factors across individuals, making the approach particularly powerful for identifying generalizable processes that account for within-population diversity (although this process can be challenging even on the single-subject level; see Kazdin, 1981 ). Single-subject methodology has historically established some of the most generalizable findings in psychology including the principles of Pavlovian and operant conditioning (Iversen, 2013 ). Establishing this generalizability requires a research program rather than a single study, however since each replication (and comparisons between them) can potentially add information about important contextual variables, systematic progression toward generality can be more efficient than in one-shot group studies.

Single-subject designs are sometimes confused with within-subject group comparisons or n-of-1 case studies, neither of which usually include multiple implementations of each condition for any one individual. N-of-1 case studies sometimes make no manipulation at all or may make a single comparison (as with an embedded AB design or pre-post observation), which can at best serve as a quasi-experiment (Kazdin and Tuma, 1982 ). A single subject design, in contrast, will include many repeated condition changes and collect multiple data points inside each condition (as in the ABABABAB design as well as many others, see Perone, 1991 ). As is the case for group designs, the quality of evidence in a single-subject experiment increases with the number of instances in which the experimental condition is compared to a control condition; the more comparisons occur, the less likely it is that an alternative explanation will have tracked with the manipulation. A strong single-subject design will require a minimum of three IV implementations for the same individual (i.e., ABABAB, with multiple data points for each A and each B), and a robust effect will require many more.

Because single-subject designs implement conditions across time, they are susceptible to some important limitations including sequence, maturation, and exposure effects. The need to consider within-condition stability, serial dependence in data sets, reversibility, carryover effects, and long experimental time courses can also complicate these designs. Still, manipulations common in neuroscience research is often amenable to these challenges (Soto, 2020 ). Single-subject designs for phenomena that are not reversable (such as skill acquisition) can also be studied using approaches such as the within-subject multiple baseline. Multiple baselines experiments across behaviors, across cell populations, or across homotopic brain regions may be reasonable if independence can be established (Soto, 2020 ). A variety of single-subject methods are available that can help to address the unique strengths and limitations in single-subject methodology; the reader is encouraged to explore the variety of designs that cannot be enumerated in the scope of the current paper (Horner and Baer, 1978 ; Hains and Baer, 1989 ; Perone, 1991 ; Holcombe et al., 1994 ; Edgington, 1996 ; Kratochwill et al., 2010 ; Ward-Horner and Sturmey, 2010 ).

2.3. A note about statistical methods

Issues relating to statistical analysis are commonly erroneously conflated with group experimental design per se . Problems with the frequentist statistical approach commonly used in group designs has greatly impacted its efficacy; frequentist statistical methods carry limitations that have been treated thoroughly elsewhere [e.g., the generic problems with null-hypothesis statistical testing NHST (Branch, 2014 ), the inappropriate use of frequentist statistics contrary to their best use and design (Moen et al., 2016 ; Wasserstein and Lazar, 2016 ), and the inappropriate reliance on p -values (Wasserstein and Lazar, 2016 )]. I do not expand on these issues in my summary of group design because such critiques need not apply to all between-group comparisons. The use and applicability of analysis techniques are separable from the experimental utility of group designs in general, which are not limited to inferential statistics. Group experiments can also be analyzed using alternative, less problematic statistical approaches such as the probability of replication statistic or P-rep (Killeen, 2015 ) and Bayesian approaches (Berry and Stangl, 2018 ). Well-considered statistical best practices for various forms of group analysis (e.g., Moen et al., 2016 ) can help a researcher to address limitations.

The conflation of statistical methods with group designs has also led to the misconception that single-subject designs cannot be analyzed statistically. Most scientists have less familiarity with statistical analyses appropriate for use in single-subject designs and the serially-dependent data sets that they produce. While pronounced effects uncovered in single-subject experiments can often be clearly detected using appropriate visual analysis, rigorous statistical methods applicable to single-subject designs are also available (e.g., Parker and Brossart, 2003 ; Scruggs and Mastropieri, 2013 ).

3. Single-subject design and the inductive process

The advantages highlighted above suggest not only compatibility between single-subject and group approaches, but a potential advantage conferred by an order of operations between methods. Early in the research process, inductive inference based on single-subject manipulations are ideal to generate likely and testable abstractions (Russell, 1962 ). Using single-subject approaches for this inductive phase requires fewer resources compared to fully powered group approaches and can be more rigorous than small-n group pilots. An effect can be isolated in one individual, then systematically replicated across relevant differences and contexts until it fails to replicate, at which time explanatory variables can be adjusted until replicated results are produced. The altered experiment can then be analyzed in comparison to previous experiments to form a more general understanding that can be tested in a new series of experiments. After sufficient systematic replication, hybrid and group designs can assess the extent to which inductively and contextually informed abstractions generalize across the widest relevant populations.

4. Precedent of within-subject methods

Although within-subject group experiments are common in human neuroscience and psychology, e.g., Greenwald ( 1976 ) and Crockett and Fehr ( 2014 ), full-fledged single-subject designs are virtually unknown in many subfields. Still, high-impact neuroscience experiments have occasionally either implicitly or deliberately implemented within-subject reversals, demonstrating the power of these approaches to advance the science. To name just a few high-impact examples, Hodgkin et al. ( 1952 ) classic work on voltage clamping utilizing the giant squid neuron involved multiple parametric IV implementations on single neurons. The discovery of circadian rhythms in humans also involved systematic single-subject experiments comparing circadian patterns at various light intensities, light-dark schedules, and control contexts, which allowed investigators to establish that outside entrainment overrode the cycle-altering effects of different light intensities (Aschoff, 1965 ). This fruitful precedent of single-subject-like experiments at the very foundation of historical neuroscience together with the well-established efficacy of single-subject design in other fields imply that the wider adoption of the full methodology can succeed.

5. Single-subject design and individuality in neuroscience

As suggested earlier in this paper, individual variation dominates the scene in behavioral and brain sciences and constitutes a basic part of the evolutionary selection processes that shaped them. In human neuroscience, individual developmental and experience-dependent variation are of particular importance. Human brains are so individuated that functional units across individuals cannot be discerned via typical anatomical landmarks, and even between-group designs often need to utilize individuated or normalized measures (Brett et al., 2002 ; Dworetsky et al., 2021 ; Fedorenko, 2021 ; Hanson, 2022 ). A shift toward including rigorous single-subject research therefore holds particular promise for the field. For example, systematically replicated individual analyses of functional brain networks and their dynamics may more easily lead to generalizable ideas about how they develop and change, and these purportedly general processes could in turn be tested across individual contexts.

6. Time and resource logistics

Group methodology often requires great time and resources in order to produce properly powered experiments. This can lead to problems with rigor, particularly in contexts of limited funding and publish-or-perish job demands (Bernard, 2016 ; Button, 2016 ). Especially in early stages of research, single-subject methodology enables experimenters to investigate effects more critically and rigorously for each subject, to more quickly answer and refine questions in individuals first before systematically exploring the generality of findings or the importance of context, and to do so in a cost-effective way. Thus, both cost and rigor could be served by conscientiously adding single-subject methodology to the neuroscience toolbelt.

7. Suggestions for neuroscience subfields that could benefit

Cognitive, behavioral, social, and developmental neuroscience each deal with individual variation in which later stages are often dependent on earlier stages and seek to identify generalizable processes that produce variant outcomes: a task for which the single-subject and multi-method approach is ideal. Neurology and clinical neuroscience also stand to benefit from a more rigorous tool for investigating clinical cases or rare phenomena. While I do not mean to suggest that the method's utility should be limited to these subfields, the potential benefit seems particularly pronounced.

8. Discussion

In summary, greater utilization of single-subject research in human neuroscience can complement current methods by balancing the progression toward internal and then external validity and enabling a low-cost and flexible inductive process that can strengthen subsequent between-group studies. These methods have already been incidentally utilized in important neuroscience research, and they could be an even more powerful, thorough, cost-efficient, rigorous, and deliberate ingredient of an ideal approach to studying the generalizable processes that account for the highly individuated human brain and the behavior that it enables.

Author contributions

AB conceived of and wrote this manuscript.

Acknowledgments

The author would like to thank Daniele Ortu, Ph.D. for helpful comments.

Funding Statement

AB was funded by the Beatrice H. Barrett endowment for research on neuro-operant relations.

1 This discussion intentionally excludes assignment to groups based on non-manipulable variables because of the qualitative difference between correlational approaches and true experimental approaches that manipulates the IV. The former carries a very different set of considerations outside the scope of this paper.

2 If the biological process under investigation actually occurs at the population level (e.g. natural selection), the population parameter precisely applies to the question at hand. However, group comparisons are more often used to study processes that function on the individual level.

Conflict of interest

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Alnahdi G. H. (2015). Single-subject designs in special education: advantages and limitations . J. Res. Special Educ. Needs 15 , 257–265. 10.1111/1471-3802.12039 [ CrossRef ] [ Google Scholar ]
Aschoff J. (1965). Circadian rhythms in man: a self-sustained oscillator with an inherent frequency underlies human 24-hour periodicity . Science 148 , 1427–1432. 10.1126/science.148.3676.1427 [ PubMed ] [ CrossRef ] [ Google Scholar ]
Bernard C. (2016). Scientific rigor or rigor mortis? Eneuro 3 , 5–48. 10.1523/ENEURO.0176-16.2016 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Berry D. A., Stangl D. (2018). Bayesian Biostatistics . Boca Raton, FL: CRC Press. [ Google Scholar ]
Branch M. (2014). Malignant side effects of null-hypothesis significance testing . Theory Psychol. 24 , 256–277. 10.1177/0959354314525282 [ CrossRef ] [ Google Scholar ]
Brett M., Johnsrude I. S., Owen A. M. (2002). The problem of functional localization in the human brain . Nat. Rev. Neurosci. 3 , 243–249. 10.1038/nrn756 [ PubMed ] [ CrossRef ] [ Google Scholar ]
Button K. S. (2016). Statistical rigor and the perils of chance . Eneuro 3 , e30. 10.1523/ENEURO.0030-16.2016 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Button K. S., Ioannidis J. P., Mokrysz C., Nosek B. A., Flint J., Robinson E. S., et al.. (2013). Power failure: why small sample size undermines the reliability of neuroscience . Nat. Rev. Neurosci. 14 , 365–376. 10.1038/nrn3475 [ PubMed ] [ CrossRef ] [ Google Scholar ]
Byiers B. J., Reichle J., Symons F. J. (2012). Single-subject experimental design for evidence-based practice . Am. J. Speech Lang. Pathol. 21 , 397–414. 10.1044/1058-0360(2012/11-0036) [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Crockett M. J., Fehr E. (2014). Social brains on drugs: tools for neuromodulation in social neuroscience . Soc. Cogn. Affect. Neurosci. 9 , 250–254. 10.1093/scan/nst113 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Dworetsky A., Seitzman B. A., Adeyemo B., Nielsen A. N., Hatoum A. S., Smith D. M., et al.. (2021). Two common and distinct forms of variation in human functional brain networks . bioRxiv 2021.2009. 2017.460799 . 10.1101/2021.09.17.460799 [ CrossRef ] [ Google Scholar ]
Edgington E. S. (1996). Randomized single-subject experimental designs . Behav. Res. Ther. 34 , 567–574. 10.1016/0005-7967(96)00012-5 [ PubMed ] [ CrossRef ] [ Google Scholar ]
Fedorenko E. (2021). The early origins and the growing popularity of the individual-subject analytic approach in human neuroscience . Curr. Opin. Behav. Sci. 40 , 105–112. 10.1016/j.cobeha.2021.02.023 [ CrossRef ] [ Google Scholar ]
Greenwald A. G. (1976). Within-subjects designs: To use or not to use? Psychol. Bull. 83 , 314. 10.1037/0033-2909.83.2.314 [ CrossRef ] [ Google Scholar ]
Grossman J., Mackenzie F. J. (2005). The randomized controlled trial: gold standard, or merely standard? Perspect. Biol. Med. 48 , 516–534. 10.1353/pbm.2005.0092 [ PubMed ] [ CrossRef ] [ Google Scholar ]
Hains A. H., Baer D. M. (1989). Interaction effects in multielement designs: Inevitable, desirable, and ignorable . J. Appl. Behav. Analy. 22 , 57–69. 10.1901/jaba.1989.22-57 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Hanson S. J. (2022). The failure of blobology: FMRI misinterpretation, maleficience and muddle . Front. Hum. Neurosci. 16 , 205. 10.3389/fnhum.2022.870091 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Henrich J., Heine S. J., Norenzayan A. (2010). The weirdest people in the world? Behav. Brain Sci. 33 , 61–83. 10.1017/S0140525X0999152X [ PubMed ] [ CrossRef ] [ Google Scholar ]
Hodgkin A. L., Huxley A. F., Katz B. (1952). Measurement of current-voltage relations in the membrane of the giant axon of Loligo . J. Physiol. 116 , 424–448. 10.1113/jphysiol.1952.sp004716 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Holcombe A., Wolery M., Gast D. L. (1994). Comparative single-subject research: Description of designs and discussion of problems . Topics Early Childh. Special Educ. 14 , 119–145. 10.1177/027112149401400111 [ CrossRef ] [ Google Scholar ]
Horner R. D., Baer D. M. (1978). Multiple-probe technique: a variation of the multiple baseline 1 . J. Appl. Behav. Analy. 11 , 189–196. 10.1901/jaba.1978.11-189 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Hull D. L. (1988). Science as a Process: An Evolutionary Account of the Social and Conceptual Development of Science . Chicago: University of Chicago Press. 10.7208/chicago/9780226360492.001.0001 [ CrossRef ] [ Google Scholar ]
Iversen I. H. (2013). “Single-case research methods: an overview,” in APA handbook of behavior analysis: Methods and principles , ed. G. J. Madden (New York, NY: American Psychological Association; ). 10.1037/13937-001 [ CrossRef ] [ Google Scholar ]
Janosky J. E., Leininger S. L., Hoerger M. P., Libkuman T. M. (2009). Single Subject Designs in Biomedicine. Cham: Springer Science and Business Media. 10.1007/978-90-481-2444-2 [ CrossRef ] [ Google Scholar ]
Kazdin A. E. (1981). External validity and single-case experimentation: Issues and limitations (a response to JS Birnbrauer) . Analy. Interv. Dev. Disab. 1 , 133–143. 10.1016/0270-4684(81)90027-6 [ CrossRef ] [ Google Scholar ]
Kazdin A. E. (2011). “Additional design options,” in Single-Case Research Designs , ed. A. E. Kazdin (New York: Oxford Press; ), 227–256. [ Google Scholar ]
Kazdin A. E., Tuma A. H. (1982). Single-Case Research Designs . San Francisco: Jossey Bass. [ Google Scholar ]
Killeen P. R. (2015). P rep, the probability of replicating an effect . Encyclop. Clin. Psychol. 4 , 2201–2208. 10.1002/9781118625392.wbecp030 [ CrossRef ] [ Google Scholar ]
Kratochwill T. R., Hitchcock J., Horner R. H., Levin J. R., Odom S., Rindskopf D., et al.. (2010). Single-case designs technical documentation . What works clearinghouse. Technical paper. [ Google Scholar ]
Kravitz R. L., Duan N., Braslow J. (2004). Evidence-based medicine, heterogeneity of treatment effects, and the trouble with averages . Milbank Q. 82 , 661–687. 10.1111/j.0887-378X.2004.00327.x [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Kuhn T. S., Hacking I. (2012). The Structure of Scientific Revolutions. Chicago; London: The University of Chicago Press. 10.7208/chicago/9780226458144.001.0001 [ CrossRef ] [ Google Scholar ]
Lakatos I. (1978). The Methodology of Scientific Research Programmes. Cambridge; New York: Cambridge University Press. 10.1017/CBO9780511621123 [ CrossRef ] [ Google Scholar ]
Meldrum M. L. (2000). A brief history of the randomized controlled trial: From oranges and lemons to the gold standard . Hematol. Oncol. Clin. North Am. 14 , 745–760. 10.1016/S0889-8588(05)70309-9 [ PubMed ] [ CrossRef ] [ Google Scholar ]
Miller C. J., Smith S. N., Pugatch M. (2020). Experimental and quasi-experimental designs in implementation research . Psychiat. Res. 283 , 112452. 10.1016/j.psychres.2019.06.027 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Moen E. L., Fricano-Kugler C. J., Luikart B. W., O'Malley A. J. (2016). Analyzing clustered data: why and how to account for multiple observations nested within a study participant? PLoS ONE 11 , e0146721. 10.1371/journal.pone.0146721 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Parker R. I., Brossart D. F. (2003). Evaluating single-case research data: A comparison of seven statistical methods . Behav. Ther. 34 , 189–211. 10.1016/S0005-7894(03)80013-8 [ CrossRef ] [ Google Scholar ]
Perdices M., Tate R. L. (2009). Single-subject designs as a tool for evidence-based clinical practice: Are they unrecognised and undervalued? Neuropsychol. Rehabilit. 19 , 904–927. 10.1080/09602010903040691 [ PubMed ] [ CrossRef ] [ Google Scholar ]
Perone M. (1991). Experimental design in the analysis of free-operant behavior . Techn. Behav. Neur. Sci. 6 , 135–171. [ Google Scholar ]
Russell B. (1962). The Scientific Outlook. New York, NY: Norton. [ Google Scholar ]
Scruggs T. E., Mastropieri M. A. (2013). PND at 25: Past, present, and future trends in summarizing single-subject research . Remed. Special Educ. 34 , 9–19. 10.1177/0741932512440730 [ CrossRef ] [ Google Scholar ]
Sidman M. (1960). Tactics of Scientific Research . New York: Basic Books. [ Google Scholar ]
Soto P. L. (2020). Single-case experimental designs for behavioral neuroscience . J. Exper. Analy. Behav. 114 , 447–467. 10.1002/jeab.633 [ PubMed ] [ CrossRef ] [ Google Scholar ]
Tankersley M., McGoey K. E., Dalton D., Rumrill Jr P. D., Balan C. M. (2006). Single subject research methods in rehabilitation . Work 26 , 85–92. [ PubMed ] [ Google Scholar ]
Ward-Horner J., Sturmey P. (2010). Component analyses using single-subject experimental designs: A review . J. Appl. Behav. Analy. 43 , 685–704. 10.1901/jaba.2010.43-685 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
Wasserstein R. L., Lazar N. A. (2016). The ASA statement on p-values: context, process, and purpose . Am. Statist. 70 , 129–133. 10.1080/00031305.2016.1154108 [ CrossRef ] [ Google Scholar ]
Williams B. A. (2010). Perils of evidence-based medicine . Perspect. Biol. Med. 53 , 106–120. 10.1353/pbm.0.0132 [ PubMed ] [ CrossRef ] [ Google Scholar ]

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10.2 Single-Subject Research Designs

Learning objectives.

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.3 “Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research” , which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.3 “Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research” represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

Figure 10.3 Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behavior. Specifically, the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy (Sidman, 1960). The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The study by Hall and his colleagues was an ABAB reversal design. Figure 10.4 “An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design” approximates the data for Robbie. The percentage of time he spent studying (the dependent variable) was low during the first baseline phase, increased during the first treatment phase until it leveled off, decreased during the second baseline phase, and again increased during the second treatment phase.

Figure 10.4 An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design

Why is the reversal—the removal of the treatment—considered to be necessary in this type of design? Why use an ABA design, for example, rather than a simpler AB design? Notice that an AB design is essentially an interrupted time-series design applied to an individual participant. Recall that one problem with that design is that if the dependent variable changes after the treatment is introduced, it is not always clear that the treatment was responsible for the change. It is possible that something else changed at around the same time and that this extraneous variable is responsible for the change in the dependent variable. But if the dependent variable changes with the introduction of the treatment and then changes back with the removal of the treatment, it is much clearer that the treatment (and removal of the treatment) is the cause. In other words, the reversal greatly increases the internal validity of the study.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a developmentally disabled child, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades.

One solution to these problems is to use a multiple-baseline design , which is represented in Figure 10.5 “Results of a Generic Multiple-Baseline Study” . In one version of the design, a baseline is established for each of several participants, and the treatment is then introduced for each one. In essence, each participant is tested in an AB design. The key to this design is that the treatment is introduced at a different time for each participant. The idea is that if the dependent variable changes when the treatment is introduced for one participant, it might be a coincidence. But if the dependent variable changes when the treatment is introduced for multiple participants—especially when the treatment is introduced at different times for the different participants—then it is extremely unlikely to be a coincidence.

Figure 10.5 Results of a Generic Multiple-Baseline Study

Results of a Generic Multiple-Baseline Study: The multiple baselines can be for different participants, dependent variables, or settings. The treatment is introduced at a different time on each baseline

The multiple baselines can be for different participants, dependent variables, or settings. The treatment is introduced at a different time on each baseline.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009). They were interested in how a school-wide bullying prevention program affected the bullying behavior of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviors they exhibited toward their peers. (The researchers used handheld computers to help record the data.) After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviors exhibited by each student dropped shortly after the program was implemented at his or her school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviors was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, Pearson’s r , and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called visual inspection . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In the top panel of Figure 10.6 , there are fairly obvious changes in the level and trend of the dependent variable from condition to condition. Furthermore, the latencies of these changes are short; the change happens immediately. This pattern of results strongly suggests that the treatment was responsible for the changes in the dependent variable. In the bottom panel of Figure 10.6 , however, the changes in level are fairly small. And although there appears to be an increasing trend in the treatment condition, it looks as though it might be a continuation of a trend that had already begun during baseline. This pattern of results strongly suggests that the treatment was not responsible for any changes in the dependent variable—at least not to the extent that single-subject researchers typically hope to see.

Figure 10.6

Visual inspection of the data suggests an effective treatment in the top panel but an ineffective treatment in the bottom panel.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001). (Note that averaging across participants is less common.) Another approach is to compute the percentage of nonoverlapping data (PND) for each participant (Scruggs & Mastropieri, 2001). This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of nonoverlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Key Takeaways

Single-subject research designs typically involve measuring the dependent variable repeatedly over time and changing conditions (e.g., from baseline to treatment) when the dependent variable has reached a steady state. This approach allows the researcher to see whether changes in the independent variable are causing changes in the dependent variable.
In a reversal design, the participant is tested in a baseline condition, then tested in a treatment condition, and then returned to baseline. If the dependent variable changes with the introduction of the treatment and then changes back with the return to baseline, this provides strong evidence of a treatment effect.
In a multiple-baseline design, baselines are established for different participants, different dependent variables, or different settings—and the treatment is introduced at a different time on each baseline. If the introduction of the treatment is followed by a change in the dependent variable on each baseline, this provides strong evidence of a treatment effect.
Single-subject researchers typically analyze their data by graphing them and making judgments about whether the independent variable is affecting the dependent variable based on level, trend, and latency.

Practice: Design a simple single-subject study (using either a reversal or multiple-baseline design) to answer the following questions. Be sure to specify the treatment, operationally define the dependent variable, decide when and where the observations will be made, and so on.

Does positive attention from a parent increase a child’s toothbrushing behavior?
Does self-testing while studying improve a student’s performance on weekly spelling tests?
Does regular exercise help relieve depression?
Practice: Create a graph that displays the hypothetical results for the study you designed in Exercise 1. Write a paragraph in which you describe what the results show. Be sure to comment on level, trend, and latency.

Fisch, G. S. (2001). Evaluating data from behavioral analysis: Visual inspection or statistical models. Behavioural Processes , 54 , 137–154.

Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behavior support. Journal of Applied Behavior Analysis , 42 , 747–759.

Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality , 9 , 227–244.

Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative.

Research Methods in Psychology Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Applied Behavior Analysis

Find Articles on a Topic

Two Ways to Find Single Subject Research Design (SSRD) Articles

Finding ssrd articles via the browsing method, finding ssrd articles via the searching method.

Search by Article Citation in OneSearch
Find Reading Lists (AKA 'Course Reserves')
Get Articles We Don't Have through Interlibrary Loan
Browse ABA Journals
APA citation style
Install LibKey Nomad

Types of Single Subject Research Design

Types of SSRDs to look for as you skim abstracts:

reversal design
withdrawal design
ABAB design
A-B-A-B design
A-B-C design
A-B-A design
multiple baseline
alternating treatments design
multi-element design
changing criterion design
single case design
single subject design
single case series

Behavior analysts recognize the advantages of single-subject design for establishing intervention efficacy. Much of the research performed by behavior analysts will use SSRD methods.

When you need to find SSRD articles, there are two methods you can use:

Click on a title from the list of ABA Journal Titles .
Scroll down on the resulting page to the View Online section.
Choose a link which includes the date range you're interested in.
Click on a link to an issue (date) you want to explore.
From the resulting Table of Contents, explore titles of interest, reading the abstract carefully for signs that the research was carried out using a SSRD. (To help, look for the box on this page with a list of SSRD types.)

Description: PsycInfo is a key database in the field of psychology. Includes information of use to psychologists, students, and professionals in related fields such as psychiatry, management, business, and education, social science, neuroscience, law, medicine, and social work. Time Period: 1887 to present Sources: Indexes more than 2,500 journals. Subject Headings: Education, Mobile, Psychology, Social Sciences (Psychology) Scholarly or Popular: Scholarly Primary Materials: Journal Articles Information Included: Abstracts, Citations, Linked Full Text FindIt@BALL STATE: Yes Print Equivalent: None Publisher: American Psychological Association Updates: Monthly Number of Simultaneous Users: Unlimited

First , go to APA PsycInfo.

Second , copy and paste this set of terms describing different types of SSRDs into an APA PsycInfo search box, and choose "Abstract" in the drop-down menu.

Third , copy and paste this list of ABA journals into another search box in APA PsycInfo, and choose "SO Publication Name" in the drop-down menu.

Drop-down menu showing: "SO Publication Name"

Fourth , type in some keywords in another APA PsycInfo search box (or two) describing what you're researching. Use OR and add synonyms or related words for the best results.

Hit SEARCH, and see what kind of results you get!

Here's an example of a search for SSRDs in ABA journals on the topic of fitness:

APA PsycInfo search with 3 boxes. 1st box: "reversal design" OR "withdrawal design" etc. 2nd box: "Analysis of Verbal Behavior" OR "Behavior Analyst" OR etc. 3rd box: exercise or physical activity or fitness

Note that the long list of terms in the top two boxes gets cut off in the screenshot - - but they're all there!

The reason this works:

To find SSRD articles, we can't just search on the phrase "single subject research" because many studies which use SSRD do not include that phrase anywhere in the text of the article; instead such articles typically specify in the abstract (and "Methods" section) what type of SSRD method was used (ex. withdrawal design, multiple baseline, or ABA design). That's why we string together all the possible descriptions of SSRD types with the word OR in between -- it enables us to search for any sort of SSRD, regardless of how it's described. Choosing "Abstract" in the drop-down menu ensures that we're focusing on these terms being used in the abstract field (not just popping up in discussion in the full-text).
To search specifically for studies carried out in the field of Applied Behavior Analysis, we enter in the titles of the ABA journals, strung together, with OR in between. The quotation marks ensure each title is searched as a phrase. Choosing "SO Publication Name" in the drop-down menu ensures that results will be from articles published in those journals (not just references to those journals).
To limit the search to a topic we're interested in, we type in some keywords in another search box. The more synonyms you can think of, the better; that ensures you'll have a decent pool of records to look through, including authors who may have described your topic differently.

Search ideas:

To limit your search to just the top ABA journals, you can use this shorter list in place of the long one above:

"Behavior Analysis in Practice" OR "Journal of Applied Behavior Analysis" OR "Journal of Behavioral Education" OR "Journal of Developmental and Physical Disabilities" OR "Journal of the Experimental Analysis of Behavior"

To get more specific, topic-wise, add another search box with another term (or set of terms), like in this example:

Four search boxes in PsycInfo. Same as above, but with a 4th box: autism OR "developmental disorders"

To search more broadly and include other psychology studies outside of ABA journals, simply remove the list of journal titles from the search, as shown here:

Search in PsycInfo without list of journal terms.

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Next: Search by Article Citation in OneSearch >>
Last Updated: Apr 24, 2024 10:40 AM
URL: https://bsu.libguides.com/appliedbehavioranalysis

10.2 Single-Subject Research Designs

Learning objectives.

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.3 "Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research" , which shows the results of a generic single-subject study. First, the dependent variable (represented on the y -axis of the graph) is measured repeatedly over time (represented by the x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.3 "Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research" represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

Figure 10.3 Results of a Generic Single-Subject Study Illustrating Several Principles of Single-Subject Research

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behavior. Specifically, the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy In single-subject research, allowing behavior to become fairly consistent from one observation to the next before changing conditions. This makes any effect of the treatment easier to detect. (Sidman, 1960). Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative. The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the reversal design A single-subject research design that begins with a baseline condition with no treatment, followed by the introduction of a treatment, and after that a return to the baseline condition. It can include additional treatment conditions and returns to baseline. , also called the ABA design The simplest reversal design, in which there is a baseline condition (A), followed by a treatment condition (B), followed by a return to baseline (A). . During the first phase, A, a baseline A condition in a single-subject research design in which the dependent variable is measured repeatedly in the absence of any treatment. Most designs begin with a baseline condition, and many return to the baseline condition at least once. is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behavior of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

The study by Hall and his colleagues was an ABAB reversal design. Figure 10.4 "An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design" approximates the data for Robbie. The percentage of time he spent studying (the dependent variable) was low during the first baseline phase, increased during the first treatment phase until it leveled off, decreased during the second baseline phase, and again increased during the second treatment phase.

Figure 10.4 An Approximation of the Results for Hall and Colleagues’ Participant Robbie in Their ABAB Reversal Design

Why is the reversal—the removal of the treatment—considered to be necessary in this type of design? Why use an ABA design, for example, rather than a simpler AB design? Notice that an AB design is essentially an interrupted time-series design applied to an individual participant. Recall that one problem with that design is that if the dependent variable changes after the treatment is introduced, it is not always clear that the treatment was responsible for the change. It is possible that something else changed at around the same time and that this extraneous variable is responsible for the change in the dependent variable. But if the dependent variable changes with the introduction of the treatment and then changes back with the removal of the treatment, it is much clearer that the treatment (and removal of the treatment) is the cause. In other words, the reversal greatly increases the internal validity of the study.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a multiple-treatment reversal design A single-subject research design in which phases that introduce different treatments are alternated. , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behavior for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

In an alternating treatments design A single-subject research design in which multiple treatments are alternated rapidly on a regular schedule. , two or more treatments are alternated relatively quickly on a regular schedule. For example, positive attention for studying could be used one day and mild punishment for not studying the next, and so on. Or one treatment could be implemented in the morning and another in the afternoon. The alternating treatments design can be a quick and effective way of comparing treatments, but only when the treatments are fast acting.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a developmentally disabled child, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades.

One solution to these problems is to use a multiple-baseline design A single-subject research design in which multiple baselines are established for different participants, different dependent variables, or different contexts and the treatment is introduced at a different time for each baseline. , which is represented in Figure 10.5 "Results of a Generic Multiple-Baseline Study" . In one version of the design, a baseline is established for each of several participants, and the treatment is then introduced for each one. In essence, each participant is tested in an AB design. The key to this design is that the treatment is introduced at a different time for each participant. The idea is that if the dependent variable changes when the treatment is introduced for one participant, it might be a coincidence. But if the dependent variable changes when the treatment is introduced for multiple participants—especially when the treatment is introduced at different times for the different participants—then it is extremely unlikely to be a coincidence.

Figure 10.5 Results of a Generic Multiple-Baseline Study

The multiple baselines can be for different participants, dependent variables, or settings. The treatment is introduced at a different time on each baseline.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009). Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behavior support. Journal of Applied Behavior Analysis , 42 , 747–759. They were interested in how a school-wide bullying prevention program affected the bullying behavior of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviors they exhibited toward their peers. (The researchers used handheld computers to help record the data.) After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviors exhibited by each student dropped shortly after the program was implemented at his or her school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviors was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, Pearson’s r , and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called visual inspection The primary approach to data analysis in single-subject research, which involves graphing the data and making a judgment as to whether and to what extent the independent variable affected the dependent variable. . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the level One factor that is considered in the visual inspection of single-subject data. The overall level of the dependent variable within a condition. of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is trend One factor that is considered in the visual inspection of single-subject data. An increase or decrease in the independent variable over several observations. , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behavior is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is latency One factor that is considered in the visual inspection of single-subject data. The time between the change in conditions and the change in the dependent variable. , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

Figure 10.6

Visual inspection of the data suggests an effective treatment in the top panel but an ineffective treatment in the bottom panel.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the t test or analysis of variance are applied (Fisch, 2001). Fisch, G. S. (2001). Evaluating data from behavioral analysis: Visual inspection or statistical models. Behavioural Processes , 54 , 137–154. (Note that averaging across participants is less common.) Another approach is to compute the percentage of nonoverlapping data A statistic sometimes used in single-subject research. The percentage of observations in a treatment condition that are more extreme than the most extreme observation in a relevant baseline condition. (PND) for each participant (Scruggs & Mastropieri, 2001). Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality , 9 , 227–244. This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of nonoverlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Key Takeaways

Single-subject research designs typically involve measuring the dependent variable repeatedly over time and changing conditions (e.g., from baseline to treatment) when the dependent variable has reached a steady state. This approach allows the researcher to see whether changes in the independent variable are causing changes in the dependent variable.
In a reversal design, the participant is tested in a baseline condition, then tested in a treatment condition, and then returned to baseline. If the dependent variable changes with the introduction of the treatment and then changes back with the return to baseline, this provides strong evidence of a treatment effect.
In a multiple-baseline design, baselines are established for different participants, different dependent variables, or different settings—and the treatment is introduced at a different time on each baseline. If the introduction of the treatment is followed by a change in the dependent variable on each baseline, this provides strong evidence of a treatment effect.
Single-subject researchers typically analyze their data by graphing them and making judgments about whether the independent variable is affecting the dependent variable based on level, trend, and latency.

Does positive attention from a parent increase a child’s toothbrushing behavior?
Does self-testing while studying improve a student’s performance on weekly spelling tests?
Does regular exercise help relieve depression?
Practice: Create a graph that displays the hypothetical results for the study you designed in Exercise 1. Write a paragraph in which you describe what the results show. Be sure to comment on level, trend, and latency.

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Single-Subject Research

44 Overview of Single-Subject Research

Learning objectives.

Explain what single-subject research is, including how it differs from other types of psychological research.
Explain who uses single-subject research and why.

What Is Single-Subject Research?

Single-subject research is a type of quantitative research that involves studying in detail the behavior of each of a small number of participants. Note that the term single-subject does not mean that only one participant is studied; it is more typical for there to be somewhere between two and 10 participants. (This is why single-subject research designs are sometimes called small- n designs, where n is the statistical symbol for the sample size.) Single-subject research can be contrasted with group research , which typically involves studying large numbers of participants and examining their behavior primarily in terms of group means, standard deviations, and so on. The majority of this textbook is devoted to understanding group research, which is the most common approach in psychology. But single-subject research is an important alternative, and it is the primary approach in some more applied areas of psychology.

Before continuing, it is important to distinguish single-subject research from case studies and other more qualitative approaches that involve studying in detail a small number of participants. As described in Chapter 6, case studies involve an in-depth analysis and description of an individual, which is typically primarily qualitative in nature. More broadly speaking, qualitative research focuses on understanding people’s subjective experience by observing behavior and collecting relatively unstructured data (e.g., detailed interviews) and analyzing those data using narrative rather than quantitative techniques. Single-subject research, in contrast, focuses on understanding objective behavior through experimental manipulation and control, collecting highly structured data, and analyzing those data quantitatively.

Assumptions of Single-Subject Research

Again, single-subject research involves studying a small number of participants and focusing intensively on the behavior of each one. But why take this approach instead of the group approach? There are several important assumptions underlying single-subject research, and it will help to consider them now.

First and foremost is the assumption that it is important to focus intensively on the behavior of individual participants. One reason for this is that group research can hide individual differences and generate results that do not represent the behavior of any individual. For example, a treatment that has a positive effect for half the people exposed to it but a negative effect for the other half would, on average, appear to have no effect at all. Single-subject research, however, would likely reveal these individual differences. A second reason to focus intensively on individuals is that sometimes it is the behavior of a particular individual that is primarily of interest. A school psychologist, for example, might be interested in changing the behavior of a particular disruptive student. Although previous published research (both single-subject and group research) is likely to provide some guidance on how to do this, conducting a study on this student would be more direct and probably more effective.

A second assumption of single-subject research is that it is important to discover causal relationships through the manipulation of an independent variable, the careful measurement of a dependent variable, and the control of extraneous variables. For this reason, single-subject research is often considered a type of experimental research with good internal validity. Recall, for example, that Hall and his colleagues measured their dependent variable (studying) many times—first under a no-treatment control condition, then under a treatment condition (positive teacher attention), and then again under the control condition. Because there was a clear increase in studying when the treatment was introduced, a decrease when it was removed, and an increase when it was reintroduced, there is little doubt that the treatment was the cause of the improvement.

A third assumption of single-subject research is that it is important to study strong and consistent effects that have biological or social importance. Applied researchers, in particular, are interested in treatments that have substantial effects on important behaviors and that can be implemented reliably in the real-world contexts in which they occur. This is sometimes referred to as social validity (Wolf, 1976) [1] . The study by Hall and his colleagues, for example, had good social validity because it showed strong and consistent effects of positive teacher attention on a behavior that is of obvious importance to teachers, parents, and students. Furthermore, the teachers found the treatment easy to implement, even in their often-chaotic elementary school classrooms.

Who Uses Single-Subject Research?

Single-subject research has been around as long as the field of psychology itself. In the late 1800s, one of psychology’s founders, Wilhelm Wundt, studied sensation and consciousness by focusing intensively on each of a small number of research participants. Herman Ebbinghaus’s research on memory and Ivan Pavlov’s research on classical conditioning are other early examples, both of which are still described in almost every introductory psychology textbook.

In the middle of the 20th century, B. F. Skinner clarified many of the assumptions underlying single-subject research and refined many of its techniques (Skinner, 1938) [2] . He and other researchers then used it to describe how rewards, punishments, and other external factors affect behavior over time. This work was carried out primarily using nonhuman subjects—mostly rats and pigeons. This approach, which Skinner called the experimental analysis of behavior —remains an important subfield of psychology and continues to rely almost exclusively on single-subject research. For excellent examples of this work, look at any issue of the Journal of the Experimental Analysis of Behavior . By the 1960s, many researchers were interested in using this approach to conduct applied research primarily with humans—a subfield now called applied behavior analysis (Baer, Wolf, & Risley, 1968) [3] . Applied behavior analysis plays an especially important role in contemporary research on developmental disabilities, education, organizational behavior, and health, among many other areas. Excellent examples of this work (including the study by Hall and his colleagues) can be found in the Journal of Applied Behavior Analysis .

Although most contemporary single-subject research is conducted from the behavioral perspective, it can in principle be used to address questions framed in terms of any theoretical perspective. For example, a studying technique based on cognitive principles of learning and memory could be evaluated by testing it on individual high school students using the single-subject approach. The single-subject approach can also be used by clinicians who take any theoretical perspective—behavioral, cognitive, psychodynamic, or humanistic—to study processes of therapeutic change with individual clients and to document their clients’ improvement (Kazdin, 1982) [4] .

Wolf, M. (1976). Social validity: The case for subjective measurement or how applied behavior analysis is finding its heart. Journal of Applied Behavior Analysis, 11 , 203–214. ↵
Skinner, B. F. (1938). T he behavior of organisms: An experimental analysis . New York, NY: Appleton-Century-Crofts. ↵
Baer, D. M., Wolf, M. M., & Risley, T. R. (1968). Some current dimensions of applied behavior analysis. Journal of Applied Behavior Analysis, 1 , 91–97. ↵
Kazdin, A. E. (1982). Single-case research designs: Methods for clinical and applied settings . New York, NY: Oxford University Press. ↵

A type of quantitative research that involves studying in detail the behavior of each of a small number of participants.

Research that involves studying large numbers of participants and examining their behavior primarily in terms of group means, standard deviations, and so on.

Referred to as treatments that have substantial effects on important behaviors and that can be implemented reliably in the real-world contexts in which they occur.

A subfield of psychology (behaviorism) that focuses exclusively on the effects of rewards, punishments, and other external factors on behavior.

An application of the principles of experimental analysis of behavior that plays an important role in contemporary research on developmental disabilities, education, organizational behavior, and health, among many other applied areas.

Research Methods in Psychology Copyright © 2019 by Rajiv S. Jhangiani, I-Chant A. Chiang, Carrie Cuttler, & Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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CREd Library , Research Design and Method

Single-Subject Experimental Design: An Overview

Cred library, julie wambaugh, and ralf schlosser.

December, 2014

DOI: 10.1044/cred-cred-ssd-r101-002

Single-subject experimental designs – also referred to as within-subject or single case experimental designs – are among the most prevalent designs used in CSD treatment research. These designs provide a framework for a quantitative, scientifically rigorous approach where each participant provides his or her own experimental control.

An Overview of Single-Subject Experimental Design

What is single-subject design.

Transcript of the video Q&A with Julie Wambaugh. The essence of single-subject design is using repeated measurements to really understand an individual’s variability, so that we can use our understanding of that variability to determine what the effects of our treatment are. For me, one of the first steps in developing a treatment is understanding what an individual does. So, if I were doing a group treatment study, I would not necessarily be able to see or to understand what was happening with each individual patient, so that I could make modifications to my treatment and understand all the details of what’s happening in terms of the effects of my treatment. For me it’s a natural first step in the progression of developing a treatment. Also with the disorders that we deal with, it’s very hard to get the number of participants that we would need for the gold standard randomized controlled trial. Using single-subject designs works around the possible limiting factor of not having enough subjects in a particular area of study. My mentor was Dr. Cynthia Thompson, who was trained by Leija McReynolds from the University of Kansas, which was where a lot of single-subject design in our field originated, and so I was fortunate to be on the cutting edge of this being implemented in our science back in the late ’70s early ’80s. We saw, I think, a nice revolution in terms of attention to these types of designs, giving credit to the type of data that could be obtained from these types of designs, and a flourishing of these designs really through the 1980s into the 1990s and into the 2000s. But I think — I’ve talked with other single-subject design investigators, and now we’re seeing maybe a little bit of a lapse of attention, and a lack of training again among our young folks. Maybe people assume that people understand the foundation, but they really don’t. And more problems are occurring with the science. I think we need to re-establish the foundations in our young scientists. And this project, I think, will be a big plus toward moving us in that direction.

What is the Role of Single-Subject Design?

Transcript of the video Q&A with Ralf Schlosser. So what has happened recently, is with the onset of evidence-based practice and the adoption of the common hierarchy of evidence in terms of designs. As you noted the randomized controlled trial and meta-analyses of randomized controlled trials are on top of common hierarchies. And that’s fine. But it doesn’t mean that single-subject cannot play a role. For example, single-subject design can be implemented prior to implementing a randomized controlled trial to get a better handle on the magnitude of the effects, the workings of the active ingredients, and all of that. It is very good to prepare that prior to developing a randomized controlled trial. After you have implemented the randomized controlled trial, and then you want to implement the intervention in a more naturalistic setting, it becomes very difficult to do that in a randomized form or at the group level. So again, single-subject design lends itself to more practice-oriented implementation. So I see it as a crucial methodology among several. What we can do to promote what single-subject design is good for is to speak up. It is important that it is being recognized for what it can do and what it cannot do.

Basic Features and Components of Single-Subject Experimental Designs

Defining Features Single-subject designs are defined by the following features:

An individual “case” is the unit of intervention and unit of data analysis.
The case provides its own control for purposes of comparison. For example, the case’s series of outcome variables are measured prior to the intervention and compared with measurements taken during (and after) the intervention.
The outcome variable is measured repeatedly within and across different conditions or levels of the independent variable.

See Kratochwill, et al. (2010)

Structure and Phases of the Design Single-subject designs are typically described according to the arrangement of baseline and treatment phases.

The conditions in a single-subject experimental study are often assigned letters such as the A phase and the B phase, with A being the baseline, or no-treatment phase, and B the experimental, or treatment phase. (Other letters are sometimes used to designate other experimental phases.) Generally, the A phase serves as a time period in which the behavior or behaviors of interest are counted or scored prior to introducing treatment. In the B phase, the same behavior of the individual is counted over time under experimental conditions while treatment is administered. Decisions regarding the effect of treatment are then made by comparing an individual’s performance during the treatment, B phase, and the no-treatment. McReynolds and Thompson (1986)

Basic Components Important primary components of a single-subject study include the following:

The participant is the unit of analysis, where a participant may be an individual or a unit such as a class or school.
Participant and setting descriptions are provided with sufficient detail to allow another researcher to recruit similar participants in similar settings.
Dependent variables are (a) operationally defined and (b) measured repeatedly.
An independent variable is actively manipulated, with the fidelity of implementation documented.
A baseline condition demonstrates a predictable pattern which can be compared with the intervention condition(s).
Experimental control is achieved through introduction and withdrawal/reversal, staggered introduction, or iterative manipulation of the independent variable.
Visual analysis is used to interpret the level, trend, and variability of the data within and across phases.
External validity of results is accomplished through replication of the effects.
Social validity is established by documenting that interventions are functionally related to change in socially important outcomes.

See Horner, et al. (2005)

Common Misconceptions

Single-Subject Experimental Designs versus Case Studies

Transcript of the video Q&A with Julie Wambaugh. One of the biggest mistakes, that is a huge problem, is misunderstanding that a case study is not a single-subject experimental design. There are controls that need to be implemented, and a case study does not equate to a single-subject experimental design. People misunderstand or they misinterpret the term “multiple baseline” to mean that because you are measuring multiple things, that that gives you the experimental control. You have to be demonstrating, instead, that you’ve measured multiple behaviors and that you’ve replicated your treatment effect across those multiple behaviors. So, one instance of one treatment being implemented with one behavior is not sufficient, even if you’ve measured other things. That’s a very common mistake that I see. There’s a design — an ABA design — that’s a very strong experimental design where you measure the behavior, you implement treatment, and you then to get experimental control need to see that treatment go back down to baseline, for you to have evidence of experimental control. It’s a hard behavior to implement in our field because we want our behaviors to stay up! We don’t want to see them return back to baseline. Oftentimes people will say they did an ABA. But really, in effect, all they did was an AB. They measured, they implemented treatment, and the behavior changed because the treatment was successful. That does not give you experimental control. They think they did an experimentally sound design, but because the behavior didn’t do what the design requires to get experimental control, they really don’t have experimental control with their design.

Single-subject studies should not be confused with case studies or other non-experimental designs.

In case study reports, procedures used in treatment of a particular client’s behavior are documented as carefully as possible, and the client’s progress toward habilitation or rehabilitation is reported. These investigations provide useful descriptions. . . .However, a demonstration of treatment effectiveness requires an experimental study. A better role for case studies is description and identification of potential variables to be evaluated in experimental studies. An excellent discussion of this issue can be found in the exchange of letters to the editor by Hoodin (1986) [Article] and Rubow and Swift (1986) [Article]. McReynolds and Thompson (1986)

Other Single-Subject Myths

Transcript of the video Q&A with Ralf Schlosser. Myth 1: Single-subject experiments only have one participant. Obviously, it requires only one subject, one participant. But that’s a misnomer to think that single-subject is just about one participant. You can have as many as twenty or thirty. Myth 2: Single-subject experiments only require one pre-test/post-test. I think a lot of students in the clinic are used to the measurement of one pre-test and one post-test because of the way the goals are written, and maybe there’s not enough time to collect continuous data.But single-case experimental designs require ongoing data collection. There’s this misperception that one baseline data point is enough. But for single-case experimental design you want to see at least three data points, because it allows you to see a trend in the data. So there’s a myth about the number of data points needed. The more data points we have, the better. Myth 3: Single-subject experiments are easy to do. Single-subject design has its own tradition of methodology. It seems very easy to do when you read up on one design. But there are lots of things to consider, and lots of things can go wrong.It requires quite a bit of training. It takes at least one three-credit course that you take over the whole semester.

Clinical Research Education

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Single-Subject Research Designs

Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton

Learning Objectives

Describe the basic elements of a single-subject research design.
Design simple single-subject studies using reversal and multiple-baseline designs.
Explain how single-subject research designs address the issue of internal validity.
Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Reversal Designs

ABAB Reversal Design. Image description available.

Multiple-Baseline Designs

Multiple-Baseline Design Across Participants

Results of a Generic Multiple-Baseline Study. Image description available.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009) [2] . They were interested in how a school-wide bullying prevention program affected the bullying behavior of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviors they exhibited toward their peers. After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviors exhibited by each student dropped shortly after the program was implemented at the student’s school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviors was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

Multiple-Baseline Design Across Behaviors

Multiple-Baseline Design Across Settings

Data Analysis in Single-Subject Research

Image Description

Figure 10.2 long description: Line graph showing the results of a study with an ABAB reversal design. The dependent variable was low during first baseline phase; increased during the first treatment; decreased during the second baseline, but was still higher than during the first baseline; and was highest during the second treatment phase. [Return to Figure 10.2]

Figure 10.3 long description: Three line graphs showing the results of a generic multiple-baseline study, in which different baselines are established and treatment is introduced to participants at different times.

Figure 10.4 long description: Two graphs showing the results of a generic single-subject study with an ABA design. In the first graph, under condition A, level is high and the trend is increasing. Under condition B, level is much lower than under condition A and the trend is decreasing. Under condition A again, level is about as high as the first time and the trend is increasing. For each change, latency is short, suggesting that the treatment is the reason for the change.

Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative. ↵
Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behavior support. Journal of Applied Behavior Analysis, 42 , 747–759. ↵
Fisch, G. S. (2001). Evaluating data from behavioral analysis: Visual inspection or statistical models. Behavioral Processes, 54 , 137–154. ↵
Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality, 9 , 227–244. ↵

When the researcher waits until the participant’s behavior in one condition becomes fairly consistent from observation to observation before changing conditions.

The most basic single-subject research design in which the researcher measures the dependent variable in three phases: Baseline, before a treatment is introduced (A); after the treatment is introduced (B); and then a return to baseline after removing the treatment (A). It is often called an ABA design.

Another term for reversal design.

The beginning phase of an ABA design which acts as a kind of control condition in which the level of responding before any treatment is introduced.

In this design the baseline phase is followed by separate phases in which different treatments are introduced.

In this design two or more treatments are alternated relatively quickly on a regular schedule.

In this design, multiple baselines are either established for one participant or one baseline is established for many participants.

This means plotting individual participants’ data, looking carefully at those plots, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable.

This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition.

Single-Subject Research Designs Copyright © by Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Examples of Single-Subject Research from the Literature

(Note that each of these studies has more than one participant, but in each study they were analyzed separately, as in single subject designs.

Example # 1

Smith, R. G., & Churchill, R. M. (2002). Identification of environmental determinants of behavior disorders through functional analysis of precursor behaviors. Journal of Applied Behavior Analysis, 35 , 125-136.

The functional analysis of behavior (observing target behavior and its contingencies) has long been a major method of evaluating behavioral problems. Once a functional analysis is completed, treatment most likely entails manipulating the contingencies to strengthen or weaken the target behavior. However, this usual functional analysis procedure is seriously limited when the problem behavior poses risks for the person, as is the case with self injurious behavior (SIB). In order to analyze it, the target behavior of SIB must be allowed to occur so it and its contingencies can be observed. In that process, the person is at risk for injury due to the SIB.

In this study, the researchers focused, not on the problem behavior, such as SIB, nor on the contingencies following the behavior. Rather, they explored the possibility of looking at the behavior precursors--what the person does just prior to the appearance of the problem behavior, which may be responsible for evoking the problem behavior.

Four adults with severe cognitive disabilities and self-injurious behavior were observed individually under four different conditions in a time-series design. The four sequential conditions were:

Alone - The participant is alone and no contingencies are applied
Attention - when SIB occurs, the participant receives 5 seconds of staff attention (i.e. statements of concern or reprimand)
Play - Participant has play and game materials around; every 30 seconds staff presents a non-contingent remark, such as "How are you doing?"
Demand - Every 30 seconds staff give participant a command to perform some simple task. Verbal praise was given contingent on completion of the task.

Each participant was observed individually in each condition across a time series design. Observers made their recordings on a hand-held computer. The dependent variables (i.e., the target behaviors) were the particular problem behavior of each person (i.e., head-banging, aggression).

The results showed that, for each person, the problem behavior varied with the precursor condition, occurring more in some conditions and less in others. That is, under some conditions, the problem behavior was very low. The researchers concluded that by focusing the functional analysis on precursor conditions, it may be possible to identify the conditions under which the problem behavior is most and least likely to occur. In this way, the analysis need not include a high rate of the behavior in order to identify its contingencies. Some of the problem behavior will occur, but not as much as it does in more traditional functional analysis. This may be a way of reducing the risk of such behaviors as SIB during functional analyses.

Example # 2

Slifer, K. J,, Koontz, K. L., & Cataldo, M. (2002). Operant-conditioning-based preparation of children for functional Magnetic Resonance Imaging. Journal of Applied Behavior Analysis, 35 , 191-194.

MRI diagnoses of brain pathology is an important medical tool. The procedure most often involves cooperation of the patient, who must minimize disruptive head movements while carry out simple tasks on command. This is often difficult for children. In this study, four children, ranging in age from 7 to 10 years old, were trained using operant conditioning techniques to control disruptive head movement and to follow directions and respond effectively while in a simulated MRI procedure.

Each child moved through a multiple baseline procedure, followed by reinforcement for motor control, followed by reinforcement for accuracy in task responding. In the baseline condition, the child was given instructions, shown how to lie still, and how to respond to the tasks. In the next phase, the child was reinforced with verbal feedback, praise, and a small prize for reduced head motion. In the final phase, the child was reinforced for correct responding to the task. Note that reinforcement was contingent on motion control and performance accuracy.

Across conditions, there was a sharp improvement in head-motion control and performance accuracy as a function of the reinforcement contingencies. That is, these children became much better at cooperating during the mock MRI procedure. The researchers conclude that such training may be useful in real clinical situations to improve the validity and reliability of MRI diagnoses of children. This was a laboratory setting, using a simulated MRI procedure. Further research is needed in actual MRI settings.

Example # 3

Charlop-Christy, M. H., Carpenter, M., Loc, L., LeBlanc, L. A., & Kellet, K. (2002). Using the Picture-Exchange-Communication System (PECS) with children with autism: Assessment of PECS acquisition, speech, social communicative behavior, and problem behavior. Journal of Applied Behavior Analysis, 35, 213-231.

This research evaluates the effectiveness of a communication-training system (PECS), which is often used to teach non-speaking children with autism to communicate through a series of picture cards. Although commonly used, the procedure had not yet been effectively evaluated. This study attempted an evaluation.

In the PECS training, children are given a Velcro board and a series of cardboard pictures. Through the use of basic behavioral technology, such as differential reinforcement, shaping, and stimulus control, the child is taught to select appropriate cards and place them on the board in the desired order, thus constructing "picture sentences." In this research, three children with autism were observed across a multiple baseline design that consisted of: Pre-Training Baseline; PECS Training; Post-Training; and Follow-up.

The dependent measures were: the occurrence of spontaneous speech; the length of speech utterances; the proportion of time intervals in which the child had eye-contact with the teacher; the proportion of time intervals in which tantrums and disruptive out-of-seat behavior occurred.

The results showed that across the multiple baseline conditions, (1) all three children mastered the PECS procedure in a relatively short period, (2) all increased their amount and length of spontaneous speech; and (3) all showed a reduction of tantrum and other disruptive behavior. They concluded the PECS system is useful and effective.

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In situ observation of chemistry in Rydberg molecules within a Bose-Einstein-condensate

Felix engel, shiva kant tiwari, tilman pfau, sebastian wüster, and florian meinert, phys. rev. research 6 , 033150 – published 8 august 2024.

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INTRODUCTION
RYDBERG ELECTRON IMPRINT ON A BEC
BEC DYNAMICS AND ELECTRON STATE CHANGE
QUANTITATIVE ANALYSIS OF THE BEC…
OUTLOOK AND CONCLUSIONS
ACKNOWLEDGMENTS

We often infer the state of systems in nature indirectly, for example, in high-energy physics by the interaction of particles with an ambient medium. We adapt this principle to energies 9 orders of magnitude smaller, to classify the final state of exotic molecules after internal conversion of their electronic state, through their interaction with an ambient quantum fluid, a Bose-Einstein condensate (BEC). The BEC is the ground state of a million bosonic atoms near zero temperature, and a single embedded ultra-long-range Rydberg molecule can coherently excite waves in this fluid, which carry telltale signatures of its dynamics. Bond lengths exceeding a micrometer allow us to observe the molecular fingerprint on the BEC in situ , via optical microscopy. Interpreting images in comparison with simulations strongly suggests that the molecular electronic state rapidly converts from the initially excited S and D orbitals to a much more complex molecular state (called “trilobite”), marked by a maximally localized electron. This internal conversion liberates energy, such that one expects final-state particles to move rapidly through the medium, which is however ruled out by comparing experiment and simulations. The molecule thus must strongly decelerate in the medium, for which we propose a plausible mechanism. Our experiment demonstrates a medium that facilitates and records an electronic state change of embedded exotic molecules in ultracold chemistry, with sufficient sensitivity to constrain velocities of final-state particles.

Received 20 August 2023
Accepted 24 June 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.033150

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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1 Physikalisches Institut and Center for Integrated Quantum Science and Technology , Universität Stuttgart , Pfaffenwaldring 57, 70569 Stuttgart, Germany
2 Department of Physics, Indian Institute of Science Education and Research, Bhopal 462066, India
* These authors contributed equally to this work.
† Contact author: [email protected]
‡ Contact author: [email protected]

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Vol. 6, Iss. 3 — August - October 2024

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Rydberg excitation and subsequent electron dynamics in a BEC. (a) Single Rydberg atoms are created in the center region (red) of a cigar-shaped BEC (gray ellipsoid) using a focused laser beam (green), targeting | 133 S 〉 and | 130 D 〉 Rydberg states, with quantization axis along y . (b) Relevant molecular potential energy curves for the Rydberg electron interacting with the condensate, enabling state conversion from S ① (or D ) Rydberg orbitals via butterfly molecular states ② into trilobite molecular states ③ , with corresponding electron densities shown in orange. (c) Phase contrast image of the bare column density ρ c (density integrated along z ) after interaction of a 133 S Rydberg electron with the BEC for N Ryd = 4 repetitions at time t evol = 200 µ s . (d) Data from (c) but with the BEC background in the absence of Rydberg excitations ( ρ bg ) subtracted, yielding the change of the column density Δ ρ c = ρ c − ρ bg due to the impact of the Rydberg electron inside the marked region. (e)–(g) Numerical simulations of the expected averaged signature Δ ρ c in the ambient BEC medium when the Rydberg electron remains in the initial S state (e), transforms into a butterfly state (f) or transforms into a trilobite state (g). Each scenario causes a different imprint on the BEC, and only conversion into the trilobite state (g) explains the averaged experimental observation (h), a depression in the density instead of an increment. All simulations include a spatial uncertainty for the initial excitation of the Rydberg impurity, with standard deviations σ x , y , z = ( 0.9 , 2.6 , 0.9 ) µ m ; see panel (a).

Interactions of Rydberg electron and condensate atoms (a) Molecular potential energy curves (black and blue lines) for a single ground-state atom interacting with the Rydberg electron as a function of distance R from the ionic core. Zero energy is that of 133 S at large R . The ground-state atom is expected to follow the blue curves along the red arrows once it reaches the avoided crossing (vertical green line at R ac , s ), very likely transforming the electronic state from the initial 133 S state to the 129-trilobite state via butterfly states, based on Landau-Zener diabatic crossing probabilities shown in green. The inset shows the mean increase in the number of atoms Δ n ac (black) within the volume R < R ac and the corresponding probability P ac that at least one atom has entered this volume (red) as predicted from mean field simulations of the BEC following excitation to | S 〉 (solid) or | D 〉 (dashed). (b), (c) 2D cut at z = 0 through the 3D electron probability density for the 133 S molecular state (b) with attached condensate atom at R = 1.68 µ m , and the 129-trilobite state (c) at R = 1.58 µ m . The green (blue) circle marks the position of the Rydberg core (attached condensate atom).

Dynamical evolution of the averaged BEC density induced by Rydberg excitations to 133 S and 130 D . (a), (b) Measured (full symbols) and simulated (open symbols connected by lines) depression of the BEC density quantified by the local atom number change Δ N , of the order of a few thousand, in the Rydberg excitation region [white boxes in panels (e)–(h)]. Δ N is shown as a function of the number of sequentially implanted Rydberg atoms N Ryd with t evol = 200 µ s (a), and as a function of the time since first implantation t evol for N Ryd = 10 (b). The inset in panel (a) shows the effect of a single Rydberg excitation, the legend in panel (b) also pertains to panel (a). Simulation data depict scenarios for which the electron remains in the initially excited S state ( D state) [green in panel (b)], converts from 133 S to 129-trilobite after t conv,s = 0.7 µ s (dashed dark gray with ⋄ marked S -Tri), converts from 130 D to 128-trilobite states after t conv,d = 2 µ s (dashed light gray with ⋄ marked D -Tri), or converts into a trilobite without delay t conv,s ≈ 0 (dashed black with ⋄ marked Tril). The red-dotted boxes surround data for which details are shown exemplarily in panels (c)–(j). (e)–(h) Measured (e), (f) and simulated (g), (h) change of the column density Δ ρ c following S - and D -excitations as indicated, for N Ryd = 10 and t evol = 200 µ s . Simulation data are shown for delayed trilobite insertion (at t conv,s/d ), and account for finite optical resolution. (c), (d), (i), (j) Vertical ( y = 0 ) (c), (d) and horizontal ( x = 0 ) (i), (j) cuts through the measured (solid lines) and simulated (dashed lines) column density differences Δ ρ c , with markers below panels (c), (d) indicating the cut in panels (e)–(h). (c), (i) follow S-excitation, and (d), (j) D -excitation. (c), (d), (i), (j) Green dashed lines assume electrons staying in the initial electronic states, and gray dashed lines assume delayed conversion into trilobite molecules. Experimental data are typically averaged over 70 − 200 runs, while the simulations are averaged over 200 samples, the standard error of which is indicated by colored shading in panels (c), (d), (i), (j). Error bars in panels (a), (b) show one standard error.

Averaged density depression following repeated | S 〉 Rydberg excitations in a BEC. (a), (c), (e), (g) The relative column density in the experiment for N Ryd repeated excitations as indicated, at t evol = 200 µ s , and (b), (d), (f), (h) row-wise matching simulation results for the same, assuming conversion to the trilobite molecule from the initial | S 〉 state after 0.7 µ s .

Averaged density depression following repeated | S 〉 Rydberg excitations in a BEC. The same as Fig. 4 , but at fixed N Ryd = 10 for different wait times.

Averaged density depression following repeated | D 〉 Rydberg excitations in a BEC. (a), (c), (e) The relative column density in the experiment for N Ryd repeated excitations as indicated, at t evol = 200 µ s , and (b), (d), (f) row-wise matching simulation results for the same, assuming conversion to the trilobite molecule from the initial | D 〉 state after 2 µ s .

Averaged density depression following repeated | D 〉 Rydberg excitations in a BEC. The same as Fig. 6 , but at fixed N Ryd = 10 for different wait times.

Expected signature of moving trilobite molecules. Averaged density depression, after excitation of | S 〉 states for N Ryd = 4 and t evol = 200 µ s . (a) Relative column density change Δ ρ c from simulation with trilobites inserted at t = 0 with random orientation and moving with v = 0.5 m/s in the direction of their internuclear axis, does not agree with the experiment in panel (b). (c) Horizontal ( x = 0 ) and (d) vertical ( y = 0 ) cuts through the measured (black) and simulated (red) column density changes Δ ρ c .

Approximate potential for Rydberg D state interacting with condensate. (a) V ryd ( d ) ( R ) in the x − y plane, where the quantization axis is along y . (b) Zoom of the same near the avoided crossing, indicated by the green circle in panels (a), (b). Here we apply Gaussian smoothing with kernel width σ = 0.05 µ m to focus on the net trend of the potential. (c) Gradient of the smoothed potential near the avoided crossing shown as arrows, to capture the net trend of ∇ V ryd ( d ) ( R ) .

Multiple condensate atoms interacting with the Rydberg electron. (a) Potential with N g = 86 additional atoms on the z axis (blue and violet lines, with blue following the asymptotic | 133 S 〉 state), compared to a single atom potential (red dashed lines), 1 / 3 of the potential for a moving cluster of three atoms (black lines), and in the inset the corresponding average of three single atom potentials (green dotted line). The inset shows the outer orbital region representing the by far largest volume fraction, where many- and single-body potentials nearly agree, and even moving clusters do not cause qualitative deviations. The main panel shows the inner volume near the shape resonance. Deviations between many-body potential (blue) and single-body potential (red dashed) are visible and could strongly alter Landau-Zener crossing rates. Deviations are even stronger for the moving cluster (black), which leads to an earlier onset of the butterfly crossing, but a shallower slope. (b) Fractional s character f s ( Z 1 , Z 2 ) for two atoms on the z axis. Between the magenta lines, the s content of the initially excited state drops from 0.99 to 0.03. Again potentials are additive, unless both atoms approach R a c together.

Electron strip-off from moving attached atoms. (a) Rydberg potentials from Eq. ( C2 ), zooming near R ≈ r orb (vertical red dotted line) at the energy range in which the trilobite molecular potential connects to the hydrogenic manifold | 129 Hyd 〉 , in the presence (black) and absence (blue) of three extra perturbers fixed at z = 1.2 , 1.429 , 1.68 µ m , marked by green dotted vertical lines in panel (a), and green dots in panels (b)–(d). The position of a fourth perturber is scanned along R . The zero of energy is that of | 133 S 〉 . Green numbers are Landau Zener crossing probabilities as discussed in the text. (b)–(d) Electron density in the x − z plane, for the states marked in panel (a), with fourth atom at R = 2 µ m as shown by the blue dot.

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10.1 Overview of Single-Subject Research
Single-subject research—which involves testing a small number of participants and focusing intensively on the behavior of each individual—is an important alternative to group research in psychology. Single-subject studies must be distinguished from case studies, in which an individual case is described in detail.
Single Subject Research
Single Subject Research " Single subject research (also known as single case experiments) is popular in the fields of special education and counseling. This research design is useful when the researcher is attempting to change the behavior of an individual or a small group of individuals and wishes to document that change.
Single-Subject Research Designs
Describe the basic elements of a single-subject research design. Design simple single-subject studies using reversal and multiple-baseline designs. Explain how single-subject research designs address the issue of internal validity. Interpret the results of simple single-subject studies based on the visual inspection of graphed data.
Chapter 10 Single-Subject Research
Single-subject research—which involves testing a small number of participants and focusing intensively on the behavior of each individual—is an important alternative to group research in psychology. Single-subject studies must be distinguished from case studies, in which an individual case is described in detail.
10.1 Overview of Single-Subject Research
Single-subject research—which involves testing a small number of participants and focusing intensively on the behavior of each individual—is an important alternative to group research in psychology. Single-subject studies must be distinguished from qualitative research on a single person or small number of individuals.
Single Subject Research Design
Single subject research design is a type of research methodology characterized by repeated assessment of a particular phenomenon (often a behavior) over time and is generally used to evaluate interventions [ 2 ]. Repeated measurement across time differentiates single subject research design from case studies and group designs, as it facilitates ...
10.2 Single-Subject Research Designs
Learning Objectives Describe the basic elements of a single-subject research design. Design simple single-subject studies using reversal and multiple-baseline designs. Explain how single-subject research designs address the issue of internal validity. Interpret the results of simple single-subject studies based on the visual inspection of graphed data.
Single Subject Research
Through the use of numerous examples, we illustrate how single subject research designs lend themselves well to various aspects of research, including the stage of theory development (Level 1 research) and more formal and systematic tests of said theories (Level II and Level III research). We also describe how basic and expert competencies of ...
Single-Subject Research Designs
Describe the basic elements of a single-subject research design. Design simple single-subject studies using reversal and multiple-baseline designs. Explain how single-subject research designs address the issue of internal validity. Interpret the results of simple single-subject studies based on the visual inspection of graphed data.
The benefits of single-subject research designs and multi
3. Single-subject design and the inductive process The advantages highlighted above suggest not only compatibility between single-subject and group approaches, but a potential advantage conferred by an order of operations between methods. Early in the research process, inductive inference based on single-subject manipulations are ideal to generate likely and testable abstractions (Russell ...
10.2 Single-Subject Research Designs
Learning Objectives Describe the basic elements of a single-subject research design. Design simple single-subject studies using reversal and multiple-baseline designs. Explain how single-subject research designs address the issue of internal validity. Interpret the results of simple single-subject studies based on the visual inspection of graphed data.
Find Single Subject Research Articles
Includes suggested databases, search techniques for finding single subject studies, and links to ABA journals. Tips for using OneSearch to search ABA-related journals for articles using single case research design.
10.2 Single-Subject Research Designs
Learning Objectives Describe the basic elements of a single-subject research design. Design simple single-subject studies using reversal and multiple-baseline designs. Explain how single-subject research designs address the issue of internal validity. Interpret the results of simple single-subject studies based on the visual inspection of graphed data.
Single-subject research
Single-subject research is a group of research methods that are used extensively in the experimental analysis of behavior and applied behavior analysis with both human and non-human participants. This research strategy focuses on one participant and tracks their progress in the research topic over a period of time.
PDF SINGLE SUBJECT RESEARCH
What Are Single-Subject/System Designs? Single-subject designs involve in-depth quantitative study of the response of an individual or. group of individuals to an intervention or the withdrawal of that intervention (Szymanski, 1993). Basically, single-subject designs, focus on a single individual in a research sample (Alberto & Troutman, 1990 ...
Overview of Single-Subject Research
Single-subject research can be contrasted with group research, which typically involves studying large numbers of participants and examining their behavior primarily in terms of group means, standard deviations, and so on. The majority of this textbook is devoted to understanding group research, which is the most common approach in psychology.
Single-Subject Experimental Design: An Overview
DOI: 10.1044/cred-cred-ssd-r101-002 Single-subject experimental designs - also referred to as within-subject or single case experimental designs - are among the most prevalent designs used in CSD treatment research. These designs provide a framework for a quantitative, scientifically rigorous approach where each participant provides his or her own experimental control.
Single-Subject Research Designs
Learning Objectives Describe the basic elements of a single-subject research design. Design simple single-subject studies using reversal and multiple-baseline designs. Explain how single-subject research designs address the issue of internal validity. Interpret the results of simple single-subject studies based on the visual inspection of graphed data.
Examples of Single-Subject Research
This research evaluates the effectiveness of a communication-training system (PECS), which is often used to teach non-speaking children with autism to communicate through a series of picture cards.
Phys. Rev. Research 6, 033150 (2024)
We often infer the state of systems in nature indirectly, for example, in high-energy physics by the interaction of particles with an ambient medium. ... Phys. Rev. Research 6, 033150 - Published 8 August 2024. More. ... Single Rydberg atoms are created in the center region (red) of a cigar-shaped BEC (gray ellipsoid) ...

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