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How To Write a Statistical Analysis Essay

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Statistical analysis is a powerful tool used to draw meaningful insights from data. It can be applied to almost any field and has been used in everything from natural sciences, economics, and sociology to sports analytics and business decisions. Writing a statistical analysis essay requires an understanding of the concepts behind it as well as proficiency with data manipulation techniques.

In this guide, we’ll look at the steps involved in writing a statistical analysis essay. Experts in research paper writing from https://domypaper.me/write-my-research-paper/ give detailed instructions on how to properly conduct a statistical analysis and make valid conclusions.

Overview of statistical analysis essays

A statistical analysis essay is an academic paper that involves analyzing quantitative data and interpreting the results. It is often used in social sciences, economics and business to draw meaningful conclusions from the data. The objective of a statistical analysis essay is to analyze a specific dataset or multiple datasets in order to answer a question or prove or disprove a hypothesis. To achieve this effectively, the information must be analyzed using appropriate statistical techniques such as descriptive statistics, inferential statistics, regression analysis and correlation analysis.

Researching the subject matter

Before writing your statistical analysis essay it is important to research the subject matter thoroughly so that you have an understanding of what you are dealing with. This can include collecting and organizing any relevant data sets as well as researching different types of statistical techniques available for analyzing them. Furthermore, it is important to become familiar with the terminology associated with statistical analysis such as mean, median and mode.

Structuring your statistical analysis essay

The structure of your essay will depend on the type of data you are analyzing and the research question or hypothesis that you are attempting to answer. Generally speaking, it should include an introduction which introduces the research question or hypothesis; a body section which includes an overview of relevant literature; a description of how the data was collected and analyzed and any conclusions drawn from it; and finally a conclusion which summarizes all findings.

Analyzing data and drawing conclusions from it

After collecting and organizing your data, you must analyze it in order to draw meaningful conclusions from it. This involves using appropriate statistical techniques such as descriptive statistics, inferential statistics, regression analysis and correlation analysis. It is important to understand the assumptions made when using each technique in order to analyze the data correctly and draw accurate conclusions from it. When choosing a statistical technique for your research, it is important to consult with an expert https://typemyessay.me/service/research-paper-writing-service who can guide you on the most appropriate approach for your study.

Interpreting results and writing a conclusion

Once you have analyzed the data successfully, you must interpret the results carefully in order to answer your research question or prove/disprove your hypothesis. This involves making sure that any conclusions drawn are soundly based on the evidence presented. After interpreting the results, you should write a conclusion which summarizes all of your findings.

Using sources in your analysis

In order to back up your claims and provide support for your arguments, it is important to use credible sources within your analysis. This could include peer-reviewed articles, journals and books which can provide evidence to support your conclusion. It is also important to cite all sources used in order to avoid plagiarism.

Proofreading and finalizing your work

Once you have written your essay it is important to proofread it carefully before submitting it. This involves checking for grammar, spelling and punctuation errors as well as ensuring that the flow of the essay makes sense. Additionally, make sure that any references cited are correct and up-to-date. If you find it hard to complete your research statistical paper, you may want to consider buying a research paper for sale . This service can save you time and money, allowing you to focus on other important tasks.

Tips for writing a successful statistical analysis essay

Here are some tips for writing a successful statistical analysis essay:

• Research your subject matter thoroughly before writing your essay.
• Structure your paper according to the type of data you are analyzing.
• Analyze your data using appropriate statistical techniques.
• Interpret and draw meaningful conclusions from your results.
• Use credible sources to back up any claims or arguments made.
• Proofread and finalize your work before submitting it.

These tips will help ensure that your essay is well researched, structured correctly and contains accurate information. Following these tips will help you write a successful statistical analysis essay which can be used to answer research questions or prove/disprove hypotheses.

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Usually there is no good way to write a statistic. It rarely sounds good, and often interrupts the structure or flow of your writing. Oftentimes the best way to write descriptive statistics is to be direct. If you are citing several statistics about the same topic, it may be best to include them all in the same paragraph or section.

The mean of exam two is 77.7. The median is 75, and the mode is 79. Exam two had a standard deviation of 11.6.

Overall the company had another excellent year. We shipped 14.3 tons of fertilizer for the year, and averaged 1.7 tons of fertilizer during the summer months. This is an increase over last year, where we shipped only 13.1 tons of fertilizer, and averaged only 1.4 tons during the summer months. (Standard deviations were as followed: this summer .3 tons, last summer .4 tons).

Some fields prefer to put means and standard deviations in parentheses like this:

If you have lots of statistics to report, you should strongly consider presenting them in tables or some other visual form. You would then highlight statistics of interest in your text, but would not report all of the statistics. See the section on statistics and visuals for more details.

If you have a data set that you are using (such as all the scores from an exam) it would be unusual to include all of the scores in a paper or article. One of the reasons to use statistics is to condense large amounts of information into more manageable chunks; presenting your entire data set defeats this purpose.

At the bare minimum, if you are presenting statistics on a data set, it should include the mean and probably the standard deviation. This is the minimum information needed to get an idea of what the distribution of your data set might look like. How much additional information you include is entirely up to you. In general, don't include information if it is irrelevant to your argument or purpose. If you include statistics that many of your readers would not understand, consider adding the statistics in a footnote or appendix that explains it in more detail.

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• Report Writing

How to Write a Statistical Report

Last Updated: June 12, 2024 Fact Checked

This article was reviewed by Grace Imson, MA and by wikiHow staff writer, Jennifer Mueller, JD . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 410,425 times.

A statistical report informs readers about a particular subject or project. You can write a successful statistical report by formatting your report properly and including all the necessary information your readers need. [1] X Research source

A Beginner’s Guide to Statistical Report Writing

Use other statistical reports as a guide to format your own. Type your report in an easy-to-read font, include all the information that your reader needs, and present your results in a table or graph.

Formatting Your Report

• If you're completing your report for a class, your instructor or professor may be willing to show you some reports submitted by previous students if you ask.
• University libraries also have copies of statistical reports created by students and faculty researchers on file. Ask the research librarian to help you locate one in your field of study.
• You also may be able to find statistical reports online that were created for business or marketing research, as well as those filed for government agencies.
• Be careful following samples exactly, particularly if they were completed for research in another field. Different fields of study have their own conventions regarding how a statistical report should look and what it should contain. For example, a statistical report by a mathematician may look incredibly different than one created by a market researcher for a retail business.

• You typically want to have 1-inch margins around all sides of your report. Be careful when adding visual elements such as charts and graphs to your report, and make sure they don't bleed over the margins or your report may not print properly and will look sloppy.
• You may want to have a 1.5-inch margin on the left-hand side of the page if you anticipate putting your study into a folder or binder, so all the words can be read comfortably when the pages are turned.
• Don't double-space your report unless you're writing it for a class assignment and the instructor or professor specifically tells you to do so.
• Use headers to add the page number to every page. You may also want to add your last name or the title of the study along with the page number.

• Citation methods typically are included in style manuals, which not only detail how you should cite your references but also have rules on acceptable punctuation and abbreviations, headings, and the general formatting of your report.
• For example, if you're writing a statistical report based on a psychological study, you typically must use the style manual published by the American Psychological Association (APA).
• Your citation method is all the more important if you anticipate your statistical report will be published in a particular trade or professional journal.

• If you're creating your statistical report for a class, a cover sheet may be required. Check with your instructor or professor or look on your assignment sheet to find out whether a cover sheet is required and what should be included on it.
• For longer statistical reports, you may also want to include a table of contents. You won't be able to format this until after you've finished the report, but it will list each section of your report and the page on which that section starts.

• If you decide to create section headings, they should be bold-faced and set off in such a way that they stand out from the rest of the text. For example, you may want to center bold-faced headings and use a slightly larger font size.
• Make sure a section heading doesn't fall at the bottom of the page. You should have at least a few lines of text, if not a full paragraph, below each section heading before the page break.

• Check the margins around visual elements and make sure the text lines up and is not too close to the visual element. You want it to be clear where the text ends and the words associated with the visual element (such as the axis labels for a graph) begin.
• Visual elements can cause your text to shift, so you'll need to double-check your section headings after your report is complete and make sure none of them are at the bottom of a page.
• Where possible, you also want to change your page breaks to eliminate situations in which the last line of a page is the first line of a paragraph, or the first line of a page is the last line of a paragraph. These are difficult to read.

Creating Your Content

• Avoid overly scientific or statistical language in your abstract as much as possible. Your abstract should be understandable to a larger audience than those who will be reading the entire report.
• It can help to think of your abstract as an elevator pitch. If you were in an elevator with someone and they asked you what your project was about, your abstract is what you would say to that person to describe your project.
• Even though your abstract appears first in your report, it's often easier to write it last, after you've completed the entire report.

• Aim for clear and concise language to set the tone for your report. Put your project in layperson's terms rather than using overly statistical language, regardless of the target audience of your report.
• If your report is based on a series of scientific experiments or data drawn from polls or demographic data, state your hypothesis or expectations going into the project.
• If other work has been done in the field regarding the same subject or similar questions, it's also appropriate to include a brief review of that work after your introduction. Explain why your work is different or what you hope to add to the existing body of work through your research.

• Include a description of any particular methods you used to track results, particularly if your experiments or studies were longer-term or observational in nature.
• If you had to make any adjustments during the development of the project, identify those adjustments and explain what required you to make them.
• List any software, resources, or other materials you used in the course of your research. If you used any textbook material, a reference is sufficient – there's no need to summarize that material in your report.

• Start with your main results, then include subsidiary results or interesting facts or trends you discovered.
• Generally you want to stay away from reporting results that have nothing to do with your original expectations or hypotheses. However, if you discovered something startling and unexpected through your research, you may want to at least mention it.
• This typically will be the longest section of your report, with the most detailed statistics. It also will be the driest and most difficult section for your readers to get through, especially if they are not statisticians.
• Small graphs or charts often show your results more clearly than you can write them in text.

• When you get to this section of your report, leave the heavy, statistical language behind. This section should be easy for anyone to understand, even if they skipped over your results section.
• If any additional research or study is necessary to further explore your hypotheses or answer questions that arose in the context of your project, describe that as well.

• It is often the case that you see things in hindsight that would have made data-gathering easier or more efficient. This is the place to discuss those. Since the scientific method is designed so that others can repeat your study, you want to pass on to future researchers your insights.
• Any speculation you have, or additional questions that came to mind over the course of your study, also are appropriate here. Just make sure you keep it to a minimum – you don't want your personal opinions and speculation to overtake the project itself.

• For example, if you compared your study to a similar study conducted in another city the year before yours, you would want to include a citation to that report in your references.
• Cite your references using the appropriate citation method for your discipline or field of study.
• Avoid citing any references that you did not mention in your report. For example, you may have done some background reading in preparation for your project. However, if you didn't end up directly citing any of those sources in your report, there's no need to list them in your references.

• Avoid trade "terms of art" or industry jargon if your report will be read mainly by people outside your particular industry.
• Make sure the terms of art and statistical terms that you do use in your report are used correctly. For example, you shouldn't use the word "average" in a statistical report because people often use that word to refer to different measures. Instead, use "mean," "median," or "mode" – whichever is correct.

Presenting Your Data

• This is particularly important if you're submitting your report for publication in a trade journal. If the pages are different sizes than the paper you print your report on, your visual elements won't line up the same way in the journal as they do in your manuscript.
• This also can be a factor if your report will be published online, since different display sizes can cause visual elements to display differently.
• The easiest way to label your visual elements is "Figure," followed by a number. Then you simply number each element sequentially in the order in which they appear in your report.
• Your title describes the information presented by the visual element. For example, if you've created a bar graph that shows the test scores of students on the chemistry class final, you might title it "Chemistry Final Test Scores, Fall 2016."

• Make sure each visual element is large enough in size that your readers can see everything they need to see without squinting. If you have to shrink down a graph to the point that readers can't make out the labels, it won't be very helpful to them.
• Create your visual elements using a format that you can easily import into your word-processing file. Importing using some graphics formats can distort the image or result in extremely low resolution.

• For example, if you have hundreds of samples, your x axis will be cluttered if you display each sample individually as a bar. However, you can move the measure on the y axis to the x axis, and use the y axis to measure the frequency.
• When your data include percentages, only go out to fractions of a percentage if your research demands it. If the smallest difference between your subjects is two percentage points, there's no need to display more than the whole percentage. However, if the difference between your subjects comes down to hundredths of a percent, you would need to display percentages to two decimal places so the graph would show the difference.
• For example, if your report includes a bar graph of the distribution of test scores for a chemistry class, and those scores are 97.56, 97.52, 97.46, and 97.61, your x axis would be each of the students and your y axis would start at 97 and go up to 98. This would highlight the differences in the students' scores.

• Be careful that your appendix does not overwhelm your report. You don't necessarily want to include every data sheet or other document you created over the course of your project.
• Rather, you only want to include documents that reasonably expand and lead to a further understanding of your report.
• For example, when describing your methods you state that a survey was conducted of students in a chemistry class to determine how they studied for the final exam. You might include a copy of the questions the students were asked in an appendix. However, you wouldn't necessarily need to include a copy of each student's answers to those questions.

Statistical Report Outline

Community Q&A

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• ↑ https://www.ibm.com/docs/en/iotdm/11.3?topic=SSMLQ4_11.3.0/com.ibm.nex.optimd.dg.doc/11arcperf/oparcuse-r-statistical_reports.html
• ↑ https://www.examples.com/business/report/statistics-report.html
• ↑ https://collaboratory.ucr.edu/sites/g/files/rcwecm2761/files/2019-04/Final_Report_dan.pdf
• ↑ https://tex.stackexchange.com/questions/49386/what-is-the-recommended-font-to-use-for-a-statistical-table-in-an-academic-journ
• ↑ https://psychology.ucsd.edu/undergraduate-program/undergraduate-resources/academic-writing-resources/writing-research-papers/citing-references.html
• ↑ https://www.youtube.com/watch?v=kl3JOCmuil4

About This Article

Start your statistical report with an introduction explaining the purpose of your research. Then, dive into your research methods, how you collected data, and the experiments you conducted. Present you results with any necessary charts and graphs, but do not discuss or analyze the numbers -- in a statistical report, all analysis should happen in the conclusion. Once you’ve finished writing your report, draft a 200 word abstract and create a cover sheet with your name, the date, and the report title. Don’t forget to cite the appropriate references when necessary! For more formatting help, read on! Did this summary help you? Yes No

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What Is Statistical Analysis?

Statistical analysis helps you pull meaningful insights from data. The process involves working with data and deducing numbers to tell quantitative stories.

Statistical analysis is a technique we use to find patterns in data and make inferences about those patterns to describe variability in the results of a data set or an experiment. 

In its simplest form, statistical analysis answers questions about:

• Quantification — how big/small/tall/wide is it?
• Variability — growth, increase, decline
• The confidence level of these variabilities

What Are the 2 Types of Statistical Analysis?

• Descriptive Statistics:  Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 
• Inferential Statistics:  Inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests.

What’s the Purpose of Statistical Analysis?

Using statistical analysis, you can determine trends in the data by calculating your data set’s mean or median. You can also analyze the variation between different data points from the mean to get the standard deviation . Furthermore, to test the validity of your statistical analysis conclusions, you can use hypothesis testing techniques, like P-value, to determine the likelihood that the observed variability could have occurred by chance.

More From Abdishakur Hassan The 7 Best Thematic Map Types for Geospatial Data

Statistical Analysis Methods

There are two major types of statistical data analysis: descriptive and inferential. 

Descriptive Statistical Analysis

Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 

Within the descriptive analysis branch, there are two main types: measures of central tendency (i.e. mean, median and mode) and measures of dispersion or variation (i.e. variance , standard deviation and range). 

For example, you can calculate the average exam results in a class using central tendency or, in particular, the mean. In that case, you’d sum all student results and divide by the number of tests. You can also calculate the data set’s spread by calculating the variance. To calculate the variance, subtract each exam result in the data set from the mean, square the answer, add everything together and divide by the number of tests.

Inferential Statistics

On the other hand, inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests. 

There are two main types of inferential statistical analysis: hypothesis testing and regression analysis. We use hypothesis testing to test and validate assumptions in order to draw conclusions about a population from the sample data. Popular tests include Z-test, F-Test, ANOVA test and confidence intervals . On the other hand, regression analysis primarily estimates the relationship between a dependent variable and one or more independent variables. There are numerous types of regression analysis but the most popular ones include linear and logistic regression .  

Statistical Analysis Steps  

In the era of big data and data science, there is a rising demand for a more problem-driven approach. As a result, we must approach statistical analysis holistically. We may divide the entire process into five different and significant stages by using the well-known PPDAC model of statistics: Problem, Plan, Data, Analysis and Conclusion.

In the first stage, you define the problem you want to tackle and explore questions about the problem. 

2. Plan

Next is the planning phase. You can check whether data is available or if you need to collect data for your problem. You also determine what to measure and how to measure it. 

The third stage involves data collection, understanding the data and checking its quality. 

4. Analysis

Statistical data analysis is the fourth stage. Here you process and explore the data with the help of tables, graphs and other data visualizations.  You also develop and scrutinize your hypothesis in this stage of analysis. 

5. Conclusion

The final step involves interpretations and conclusions from your analysis. It also covers generating new ideas for the next iteration. Thus, statistical analysis is not a one-time event but an iterative process.

Statistical Analysis Uses

Statistical analysis is useful for research and decision making because it allows us to understand the world around us and draw conclusions by testing our assumptions. Statistical analysis is important for various applications, including:

• Statistical quality control and analysis in product development 
• Clinical trials
• Customer satisfaction surveys and customer experience research 
• Marketing operations management
• Process improvement and optimization
• Training needs 

More on Statistical Analysis From Built In Experts Intro to Descriptive Statistics for Machine Learning

Benefits of Statistical Analysis

Here are some of the reasons why statistical analysis is widespread in many applications and why it’s necessary:

Understand Data

Statistical analysis gives you a better understanding of the data and what they mean. These types of analyses provide information that would otherwise be difficult to obtain by merely looking at the numbers without considering their relationship.

Find Causal Relationships

Statistical analysis can help you investigate causation or establish the precise meaning of an experiment, like when you’re looking for a relationship between two variables.

Make Data-Informed Decisions

Businesses are constantly looking to find ways to improve their services and products . Statistical analysis allows you to make data-informed decisions about your business or future actions by helping you identify trends in your data, whether positive or negative. 

Determine Probability

Statistical analysis is an approach to understanding how the probability of certain events affects the outcome of an experiment. It helps scientists and engineers decide how much confidence they can have in the results of their research, how to interpret their data and what questions they can feasibly answer.

You’ve Got Questions. Our Experts Have Answers. Confidence Intervals, Explained!

What Are the Risks of Statistical Analysis?

Statistical analysis can be valuable and effective, but it’s an imperfect approach. Even if the analyst or researcher performs a thorough statistical analysis, there may still be known or unknown problems that can affect the results. Therefore, statistical analysis is not a one-size-fits-all process. If you want to get good results, you need to know what you’re doing. It can take a lot of time to figure out which type of statistical analysis will work best for your situation .

Thus, you should remember that our conclusions drawn from statistical analysis don’t always guarantee correct results. This can be dangerous when making business decisions. In marketing , for example, we may come to the wrong conclusion about a product . Therefore, the conclusions we draw from statistical data analysis are often approximated; testing for all factors affecting an observation is impossible.

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Statistics - List of Free Essay Examples And Topic Ideas

Statistics, as the science of collecting, analyzing, and interpreting data, plays an indispensable role in modern decision-making and knowledge generation. Essays could explore the myriad applications of statistics across various fields including healthcare, economics, and social sciences. They might delve into key statistical concepts, methods, and tools, illustrating how they help in understanding complex phenomena, making predictions, and informing policy. Discussions might also extend to the ethical considerations inherent in statistical practices, such as data integrity, privacy, and the potential for misrepresentation or bias. The discourse may also touch on the evolving landscape of statistics amid the advent of big data and computational advancements, examining how these developments are expanding the capabilities and applications of statistical analysis. We have collected a large number of free essay examples about Statistics you can find at PapersOwl Website. You can use our samples for inspiration to write your own essay, research paper, or just to explore a new topic for yourself.

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Reading through the article provided a vivid reflection on how racism becomes a serious issue in the today society. There are various types of racism the article brings out manifested in micro aggression form. The varied opinions in my mind provide a clear picture of the information relayed in the article through the following analysis. Discrimination concerning race will major in my analysis. First, let me talk about the black guy abused in the Saudi Arabia that has sparked public […]

New Insights into Modern Sports Narratives

In the realm of contemporary sports journalism a diverse array of compelling stories has surfaced each offering a distinct glimpse into the dynamic world of athletic competition and achievement. These articles go beyond mere statistics presenting nuanced narratives that resonate with the human spirit and captivate audiences worldwide. One particularly intriguing article profiles a seasoned tennis player whose remarkable comeback culminated in a historic triumph at a prestigious Grand Slam tournament. This narrative not only celebrates the athlete's perseverance and […]

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How to Write a Statistics Essay: Short Guide

Statistics is an incredibly useful subject, particularly in today's data-driven world, and it frequently goes hand in hand with tools. For example excel is renowned for its ability to handle a variety of complex calculations, making it an indispensable tool for students tackling statistical problems. However, mastering requires a solid foundation of knowledge, which some students may lack. This is where the integration of STEM-focused Excel courses in many universities becomes beneficial, providing students with the necessary skills to utilize effectively for statistical analysis. Nevertheless, when students encounter difficulties, PapersOwl presents a solution with excel help online.

Their experts are adept in both statistics, offering personalized assistance to students who struggle with using Excel for their statistical assignments.

Writing a statistics essay involves more than just presenting numbers and data. It requires a clear understanding of statistical methods, an ability to interpret results, and the skill to communicate findings effectively. This article provides a step-by-step guide on how to write a compelling statistics essay.

Understanding the Essay Question

Firstly, it's essential to comprehend the specific question or topic you are dealing with. A statistics essay could range from analyzing a set of data to discussing a particular statistical method. Understanding the scope, requirements, and objectives of the essay will guide your research and writing process.

Research and Data Collection

Begin by collecting relevant data for your essay. This could involve gathering existing data or conducting your own research. Ensure that your sources are credible and that your data is accurate. Additionally, familiarize yourself with the statistical methods that are appropriate for analyzing your data.

Planning Your Essay

Organize your thoughts and data before you start writing. This includes outlining the structure of your essay and deciding how you will present your data. A typical structure might include an introduction, a methodology section, a data analysis section, and a conclusion.

Writing the Introduction

Your introduction should set the context for your essay. Explain why the topic is important and how your essay addresses it. Introduce your thesis statement or the main argument of your essay.

Methodology

In this section, describe the methods used to collect and analyze your data. Be detailed so that readers understand how you arrived at your conclusions. This might include discussing sample sizes, variables, and statistical tests used.

Data Analysis

This is the core of your statistics essay. Present your data in a clear and structured manner. Use graphs, tables, and charts to illustrate your points. Interpret the results of your analysis, explaining what the data shows and why it is significant.

Discussing Results

Go beyond just presenting data. Discuss what the results mean in the context of your topic. Compare your findings with other studies and theories. Address any limitations in your study and suggest areas for further research.

Summarize the main points of your essay, restating your thesis in light of the evidence presented. Highlight the significance of your findings and how they contribute to the understanding of the topic.

Referencing and Citation

Accurately cite all the sources and data used in your essay. Follow the required citation style (APA, MLA, Chicago, etc.). Proper citation is essential to avoid plagiarism and to give credit to the original authors.

Proofreading and Editing

Finally, revise your essay. Check for grammatical and spelling errors, ensure clarity and flow, and verify that all data is accurately presented. Peer reviews can be helpful in identifying areas for improvement.

In conclusion, writing a statistics essay requires careful planning, thorough research, and clear presentation of data and findings. By following these guidelines, you can effectively communicate complex statistical information and insights, contributing meaningfully to the topic of discussion.

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Basic statistical tools in research and data analysis

Zulfiqar ali.

Department of Anaesthesiology, Division of Neuroanaesthesiology, Sheri Kashmir Institute of Medical Sciences, Soura, Srinagar, Jammu and Kashmir, India

S Bala Bhaskar

1 Department of Anaesthesiology and Critical Care, Vijayanagar Institute of Medical Sciences, Bellary, Karnataka, India

Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data. The results and inferences are precise only if proper statistical tests are used. This article will try to acquaint the reader with the basic research tools that are utilised while conducting various studies. The article covers a brief outline of the variables, an understanding of quantitative and qualitative variables and the measures of central tendency. An idea of the sample size estimation, power analysis and the statistical errors is given. Finally, there is a summary of parametric and non-parametric tests used for data analysis.

INTRODUCTION

Statistics is a branch of science that deals with the collection, organisation, analysis of data and drawing of inferences from the samples to the whole population.[ 1 ] This requires a proper design of the study, an appropriate selection of the study sample and choice of a suitable statistical test. An adequate knowledge of statistics is necessary for proper designing of an epidemiological study or a clinical trial. Improper statistical methods may result in erroneous conclusions which may lead to unethical practice.[ 2 ]

Variable is a characteristic that varies from one individual member of population to another individual.[ 3 ] Variables such as height and weight are measured by some type of scale, convey quantitative information and are called as quantitative variables. Sex and eye colour give qualitative information and are called as qualitative variables[ 3 ] [ Figure 1 ].

Classification of variables

Quantitative variables

Quantitative or numerical data are subdivided into discrete and continuous measurements. Discrete numerical data are recorded as a whole number such as 0, 1, 2, 3,… (integer), whereas continuous data can assume any value. Observations that can be counted constitute the discrete data and observations that can be measured constitute the continuous data. Examples of discrete data are number of episodes of respiratory arrests or the number of re-intubations in an intensive care unit. Similarly, examples of continuous data are the serial serum glucose levels, partial pressure of oxygen in arterial blood and the oesophageal temperature.

A hierarchical scale of increasing precision can be used for observing and recording the data which is based on categorical, ordinal, interval and ratio scales [ Figure 1 ].

Categorical or nominal variables are unordered. The data are merely classified into categories and cannot be arranged in any particular order. If only two categories exist (as in gender male and female), it is called as a dichotomous (or binary) data. The various causes of re-intubation in an intensive care unit due to upper airway obstruction, impaired clearance of secretions, hypoxemia, hypercapnia, pulmonary oedema and neurological impairment are examples of categorical variables.

Ordinal variables have a clear ordering between the variables. However, the ordered data may not have equal intervals. Examples are the American Society of Anesthesiologists status or Richmond agitation-sedation scale.

Interval variables are similar to an ordinal variable, except that the intervals between the values of the interval variable are equally spaced. A good example of an interval scale is the Fahrenheit degree scale used to measure temperature. With the Fahrenheit scale, the difference between 70° and 75° is equal to the difference between 80° and 85°: The units of measurement are equal throughout the full range of the scale.

Ratio scales are similar to interval scales, in that equal differences between scale values have equal quantitative meaning. However, ratio scales also have a true zero point, which gives them an additional property. For example, the system of centimetres is an example of a ratio scale. There is a true zero point and the value of 0 cm means a complete absence of length. The thyromental distance of 6 cm in an adult may be twice that of a child in whom it may be 3 cm.

STATISTICS: DESCRIPTIVE AND INFERENTIAL STATISTICS

Descriptive statistics[ 4 ] try to describe the relationship between variables in a sample or population. Descriptive statistics provide a summary of data in the form of mean, median and mode. Inferential statistics[ 4 ] use a random sample of data taken from a population to describe and make inferences about the whole population. It is valuable when it is not possible to examine each member of an entire population. The examples if descriptive and inferential statistics are illustrated in Table 1 .

Example of descriptive and inferential statistics

Descriptive statistics

The extent to which the observations cluster around a central location is described by the central tendency and the spread towards the extremes is described by the degree of dispersion.

Measures of central tendency

The measures of central tendency are mean, median and mode.[ 6 ] Mean (or the arithmetic average) is the sum of all the scores divided by the number of scores. Mean may be influenced profoundly by the extreme variables. For example, the average stay of organophosphorus poisoning patients in ICU may be influenced by a single patient who stays in ICU for around 5 months because of septicaemia. The extreme values are called outliers. The formula for the mean is

where x = each observation and n = number of observations. Median[ 6 ] is defined as the middle of a distribution in a ranked data (with half of the variables in the sample above and half below the median value) while mode is the most frequently occurring variable in a distribution. Range defines the spread, or variability, of a sample.[ 7 ] It is described by the minimum and maximum values of the variables. If we rank the data and after ranking, group the observations into percentiles, we can get better information of the pattern of spread of the variables. In percentiles, we rank the observations into 100 equal parts. We can then describe 25%, 50%, 75% or any other percentile amount. The median is the 50 th percentile. The interquartile range will be the observations in the middle 50% of the observations about the median (25 th -75 th percentile). Variance[ 7 ] is a measure of how spread out is the distribution. It gives an indication of how close an individual observation clusters about the mean value. The variance of a population is defined by the following formula:

where σ 2 is the population variance, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The variance of a sample is defined by slightly different formula:

where s 2 is the sample variance, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. The formula for the variance of a population has the value ‘ n ’ as the denominator. The expression ‘ n −1’ is known as the degrees of freedom and is one less than the number of parameters. Each observation is free to vary, except the last one which must be a defined value. The variance is measured in squared units. To make the interpretation of the data simple and to retain the basic unit of observation, the square root of variance is used. The square root of the variance is the standard deviation (SD).[ 8 ] The SD of a population is defined by the following formula:

where σ is the population SD, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The SD of a sample is defined by slightly different formula:

where s is the sample SD, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. An example for calculation of variation and SD is illustrated in Table 2 .

Example of mean, variance, standard deviation

Normal distribution or Gaussian distribution

Most of the biological variables usually cluster around a central value, with symmetrical positive and negative deviations about this point.[ 1 ] The standard normal distribution curve is a symmetrical bell-shaped. In a normal distribution curve, about 68% of the scores are within 1 SD of the mean. Around 95% of the scores are within 2 SDs of the mean and 99% within 3 SDs of the mean [ Figure 2 ].

Normal distribution curve

Skewed distribution

It is a distribution with an asymmetry of the variables about its mean. In a negatively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the right of Figure 1 . In a positively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the left of the figure leading to a longer right tail.

Curves showing negatively skewed and positively skewed distribution

Inferential statistics

In inferential statistics, data are analysed from a sample to make inferences in the larger collection of the population. The purpose is to answer or test the hypotheses. A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. Hypothesis tests are thus procedures for making rational decisions about the reality of observed effects.

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty).

In inferential statistics, the term ‘null hypothesis’ ( H 0 ‘ H-naught ,’ ‘ H-null ’) denotes that there is no relationship (difference) between the population variables in question.[ 9 ]

Alternative hypothesis ( H 1 and H a ) denotes that a statement between the variables is expected to be true.[ 9 ]

The P value (or the calculated probability) is the probability of the event occurring by chance if the null hypothesis is true. The P value is a numerical between 0 and 1 and is interpreted by researchers in deciding whether to reject or retain the null hypothesis [ Table 3 ].

P values with interpretation

If P value is less than the arbitrarily chosen value (known as α or the significance level), the null hypothesis (H0) is rejected [ Table 4 ]. However, if null hypotheses (H0) is incorrectly rejected, this is known as a Type I error.[ 11 ] Further details regarding alpha error, beta error and sample size calculation and factors influencing them are dealt with in another section of this issue by Das S et al .[ 12 ]

Illustration for null hypothesis

PARAMETRIC AND NON-PARAMETRIC TESTS

Numerical data (quantitative variables) that are normally distributed are analysed with parametric tests.[ 13 ]

Two most basic prerequisites for parametric statistical analysis are:

• The assumption of normality which specifies that the means of the sample group are normally distributed
• The assumption of equal variance which specifies that the variances of the samples and of their corresponding population are equal.

However, if the distribution of the sample is skewed towards one side or the distribution is unknown due to the small sample size, non-parametric[ 14 ] statistical techniques are used. Non-parametric tests are used to analyse ordinal and categorical data.

Parametric tests

The parametric tests assume that the data are on a quantitative (numerical) scale, with a normal distribution of the underlying population. The samples have the same variance (homogeneity of variances). The samples are randomly drawn from the population, and the observations within a group are independent of each other. The commonly used parametric tests are the Student's t -test, analysis of variance (ANOVA) and repeated measures ANOVA.

Student's t -test

Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. It is used in three circumstances:

where X = sample mean, u = population mean and SE = standard error of mean

where X 1 − X 2 is the difference between the means of the two groups and SE denotes the standard error of the difference.

• To test if the population means estimated by two dependent samples differ significantly (the paired t -test). A usual setting for paired t -test is when measurements are made on the same subjects before and after a treatment.

The formula for paired t -test is:

where d is the mean difference and SE denotes the standard error of this difference.

The group variances can be compared using the F -test. The F -test is the ratio of variances (var l/var 2). If F differs significantly from 1.0, then it is concluded that the group variances differ significantly.

Analysis of variance

The Student's t -test cannot be used for comparison of three or more groups. The purpose of ANOVA is to test if there is any significant difference between the means of two or more groups.

In ANOVA, we study two variances – (a) between-group variability and (b) within-group variability. The within-group variability (error variance) is the variation that cannot be accounted for in the study design. It is based on random differences present in our samples.

However, the between-group (or effect variance) is the result of our treatment. These two estimates of variances are compared using the F-test.

A simplified formula for the F statistic is:

where MS b is the mean squares between the groups and MS w is the mean squares within groups.

Repeated measures analysis of variance

As with ANOVA, repeated measures ANOVA analyses the equality of means of three or more groups. However, a repeated measure ANOVA is used when all variables of a sample are measured under different conditions or at different points in time.

As the variables are measured from a sample at different points of time, the measurement of the dependent variable is repeated. Using a standard ANOVA in this case is not appropriate because it fails to model the correlation between the repeated measures: The data violate the ANOVA assumption of independence. Hence, in the measurement of repeated dependent variables, repeated measures ANOVA should be used.

Non-parametric tests

When the assumptions of normality are not met, and the sample means are not normally, distributed parametric tests can lead to erroneous results. Non-parametric tests (distribution-free test) are used in such situation as they do not require the normality assumption.[ 15 ] Non-parametric tests may fail to detect a significant difference when compared with a parametric test. That is, they usually have less power.

As is done for the parametric tests, the test statistic is compared with known values for the sampling distribution of that statistic and the null hypothesis is accepted or rejected. The types of non-parametric analysis techniques and the corresponding parametric analysis techniques are delineated in Table 5 .

Analogue of parametric and non-parametric tests

Median test for one sample: The sign test and Wilcoxon's signed rank test

The sign test and Wilcoxon's signed rank test are used for median tests of one sample. These tests examine whether one instance of sample data is greater or smaller than the median reference value.

This test examines the hypothesis about the median θ0 of a population. It tests the null hypothesis H0 = θ0. When the observed value (Xi) is greater than the reference value (θ0), it is marked as+. If the observed value is smaller than the reference value, it is marked as − sign. If the observed value is equal to the reference value (θ0), it is eliminated from the sample.

If the null hypothesis is true, there will be an equal number of + signs and − signs.

The sign test ignores the actual values of the data and only uses + or − signs. Therefore, it is useful when it is difficult to measure the values.

Wilcoxon's signed rank test

There is a major limitation of sign test as we lose the quantitative information of the given data and merely use the + or – signs. Wilcoxon's signed rank test not only examines the observed values in comparison with θ0 but also takes into consideration the relative sizes, adding more statistical power to the test. As in the sign test, if there is an observed value that is equal to the reference value θ0, this observed value is eliminated from the sample.

Wilcoxon's rank sum test ranks all data points in order, calculates the rank sum of each sample and compares the difference in the rank sums.

Mann-Whitney test

It is used to test the null hypothesis that two samples have the same median or, alternatively, whether observations in one sample tend to be larger than observations in the other.

Mann–Whitney test compares all data (xi) belonging to the X group and all data (yi) belonging to the Y group and calculates the probability of xi being greater than yi: P (xi > yi). The null hypothesis states that P (xi > yi) = P (xi < yi) =1/2 while the alternative hypothesis states that P (xi > yi) ≠1/2.

Kolmogorov-Smirnov test

The two-sample Kolmogorov-Smirnov (KS) test was designed as a generic method to test whether two random samples are drawn from the same distribution. The null hypothesis of the KS test is that both distributions are identical. The statistic of the KS test is a distance between the two empirical distributions, computed as the maximum absolute difference between their cumulative curves.

Kruskal-Wallis test

The Kruskal–Wallis test is a non-parametric test to analyse the variance.[ 14 ] It analyses if there is any difference in the median values of three or more independent samples. The data values are ranked in an increasing order, and the rank sums calculated followed by calculation of the test statistic.

Jonckheere test

In contrast to Kruskal–Wallis test, in Jonckheere test, there is an a priori ordering that gives it a more statistical power than the Kruskal–Wallis test.[ 14 ]

Friedman test

The Friedman test is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for repeated measures ANOVAs which is used when the same parameter has been measured under different conditions on the same subjects.[ 13 ]

Tests to analyse the categorical data

Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. The Chi-square test compares the frequencies and tests whether the observed data differ significantly from that of the expected data if there were no differences between groups (i.e., the null hypothesis). It is calculated by the sum of the squared difference between observed ( O ) and the expected ( E ) data (or the deviation, d ) divided by the expected data by the following formula:

A Yates correction factor is used when the sample size is small. Fischer's exact test is used to determine if there are non-random associations between two categorical variables. It does not assume random sampling, and instead of referring a calculated statistic to a sampling distribution, it calculates an exact probability. McNemar's test is used for paired nominal data. It is applied to 2 × 2 table with paired-dependent samples. It is used to determine whether the row and column frequencies are equal (that is, whether there is ‘marginal homogeneity’). The null hypothesis is that the paired proportions are equal. The Mantel-Haenszel Chi-square test is a multivariate test as it analyses multiple grouping variables. It stratifies according to the nominated confounding variables and identifies any that affects the primary outcome variable. If the outcome variable is dichotomous, then logistic regression is used.

SOFTWARES AVAILABLE FOR STATISTICS, SAMPLE SIZE CALCULATION AND POWER ANALYSIS

Numerous statistical software systems are available currently. The commonly used software systems are Statistical Package for the Social Sciences (SPSS – manufactured by IBM corporation), Statistical Analysis System ((SAS – developed by SAS Institute North Carolina, United States of America), R (designed by Ross Ihaka and Robert Gentleman from R core team), Minitab (developed by Minitab Inc), Stata (developed by StataCorp) and the MS Excel (developed by Microsoft).

There are a number of web resources which are related to statistical power analyses. A few are:

• StatPages.net – provides links to a number of online power calculators
• G-Power – provides a downloadable power analysis program that runs under DOS
• Power analysis for ANOVA designs an interactive site that calculates power or sample size needed to attain a given power for one effect in a factorial ANOVA design
• SPSS makes a program called SamplePower. It gives an output of a complete report on the computer screen which can be cut and paste into another document.

It is important that a researcher knows the concepts of the basic statistical methods used for conduct of a research study. This will help to conduct an appropriately well-designed study leading to valid and reliable results. Inappropriate use of statistical techniques may lead to faulty conclusions, inducing errors and undermining the significance of the article. Bad statistics may lead to bad research, and bad research may lead to unethical practice. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important. An appropriate knowledge about the basic statistical methods will go a long way in improving the research designs and producing quality medical research which can be utilised for formulating the evidence-based guidelines.

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Conflicts of interest.

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Statistical Data Essays (Examples)

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Statistical Data Analysis of the

This analysis was deemed necessary as differences can exist on the basis of an overall group effect and not an individual variable (question) effect and visa versa. Male Mean Per Question Analysis x Department Source of Sum of d.f. Mean Variation Squares between error Required F. value: 4.21 ? Concluding Statement: With a received F. value of 1.04 and a required value of F = 4.21 the conclusion can be drawn that no statistically significant differences exist in attitude toward Career Choice, Professional Relationships and Development for male radiographer participants within the three health care departments at a probability level of 95%. Therefore, all three health care groups consisting of males perceive attitudes towards Career Choice, Professional Relationships and Development the same. Female Mean Per Question Analysis x Department Source of Sum of d.f. Mean Variation Squares between error Required F. Value: 4.21 ? Concluding Statement: With a received F. value of 0.1757 and a required value of F…...

Statistical Data Being the Driver of What

statistical data being the driver of what choice is chosen and why. The concepts that lead to the decision, the inclusion of proper probability concepts, the outcome of the decision with statistical data to back it up, the tradeoffs between accuracy and precision, and the decision itself are to be discussed in this report. The business decision that will be discussed will be whether the Hostess empire should have been shut down given the events and labor union efforts that were going on at the time. Decision Made & What Led to It One concept that had to be assessed during the Hostess drama was two-fold with both dimensions of the decision being very hard. The first part was how expensive it was per day to have the unions on strike and the probability that the strike would be stopped before it was fiscally too late to recover from the bakeries…...

mla References Feintzeig, R. (2012, November 20). Hostess Plans to Liquidate After Mediation Fails WSJ.com. The Wall Street Journal - Breaking News, Business, Financial and Economic News, World News & Video - Wall Street Journal - Wsj.com. Retrieved March 24, 2013, from   http://online.wsj.com/article/SB10001424127887323713104578131502378821868.html  McCoy, K., & Higgins, L. (2012, November 21). Hostess gets OK from judge to liquidate. USA TODAY: Latest World and U.S. News - USATODAY.com. Retrieved March 24, 2013, from   http://www.usatoday.com/story/money/2012/11/21/

Statistical Data Usage in Criminal Justice Leadership

When leaders in the field of criminal justice are going to develop, change or implement policies within their field, it is always important that these developments, changes and implementations are grounded in evidence. Evidence-based practice is universally recognized as essential to good decision making (Noe, Hollenbeck, Gerhart & Wright, 2003). In order to use the evidence, one has to obtain the evidence—and that happens by way of statistical analysis and research. Researchers who gather, assess and use statistical data to understand an issue and devise a solution to a problem are grounding their work in evidence that can be quantified. When evidence can be quantified—i.e., statistically measured—it is easier to see when policies are working and when they are not. For example, in criminal justice policy making, leaders might want to institute a new way method for police to report internally on abuses in the workplace. The method they choose,…...

Prelude to Statistical Data Analysis

Take for example a human resource manager who is interested in how three different departments in a business situation waste time on the internet on a given day when they should be doing company business. The human resource person would collect data through a time study process and determine the number of times each employee in each department logs on and off the internet for personal business. The times would be collected, added together and the times of each department converted to percentages. In the example presented, the human resource manager can report that, cumulatively, the employees in Department 1 spent a total of 5 hours a day on the Internet, Department 2 employees 2 hours a day and Department 3 spent 6 hours. The raw numeric count is then converted to percentages and the pie chart would look like the following (Ohlson, 2005): The solution to the data presented above…...

mla References Ohlson, E.L. (1998). Best Fit Statistical Practices. Chicago: ACTS Testing Labs. p.43 Weirs, Ronald M. (2005). Introduction to Business Statistics. Scranton, PA: Brooks/Cole Publishing Company. Chart/Graph

Business Statistics Statistical Data Is

Because the nature of economic and business phenomena is clearly statistical in nature and the need for a scientific approach is becoming more and more necessary, so statistical analysis has become an integral part of every aspect of theoretical and applied research. The inter-dependence of economies and the development of global markets has introduced new levels and sources of competition for the businesses. Businesses face new levels of risk as the markets in which they operate become more open. Should they invest in new capacity to be able to compete more effectively? How exposed a position can they afford to take in their key markets? In short, how does a business cope with the risks inherent in the modern economy? When uncertainty is so high, the management has no choice but make the use of the statistics to justify their decisions. So statistical devices are a set of tools that can…...

How Statistical Data Influences Evidence-Based Practice

Evidence-based practice (EBP) is defined as the conscientious, judicious, and explicit use of current best evidence to make decisions about patient care. EBP incorporates the best available evidence in order to guide nursing care and improve patient outcomes. This will assist health practitioners to address health care questions by using an evaluative and qualitative approach. EBP is a problem-solving approach to clinical practice and involves the search for and critically appraising the most relevant evidence, one\\'s clinical experience and the preferences of the patient (Fortunato, Grainger, & Abou-El-Enein, 2018). The process involved in EBP allows the practitioner to assess research, clinical guidelines, and other information resources that are based on high-quality findings and apply the results obtained to improve their practice. Since EBP heavily relies on research and searching for available evidence to support a hypothetical question in order to solve a current problem, it is vital that one understands and…...

Statistical Procedures the Study Conducted

After analyzing all the data, researchers found their hypothesis to be true. There was a significantly higher percentage of both depression and anxiety disorder within individuals with afflicted family members, "The team found a 45% increased risk for depressive disorders and a 55% increased risk for anxiety disorders among the Parkinson's relatives," (Bakalar 2007). The newly published study found that an astounding fifty percent increase in both disorders when compared to family members without the disorder. Another surprising fact found through analyzing the data was that individuals had an even higher risk of exhibiting depression and anxiety disorder when their family member had been afflicted by Parkinson's disease earlier in life than when compared to those who were afflicted with the disease later in life. This study had proven the detrimental effects of the disease on all those involved in the situation. The methodology used to analyze the data was…...

mla Works Cited Bakalar, Nicholas. (December 2007). "Patterns: Parkinson's Raises Risks of Depression In Relatives." Cohort.com. (2007). "ANOVA in CoStat (Including Experimental Designs, Unbalanced Designs, Missing Values, Multiple Comparisons of Means, Planned Contrasts, and Orthogonal Contrasts).   http://www.cohort.com/costatanova.html

Statistical Concepts Have Literally Thousands of Applications

Statistical concepts have literally thousands of applications, but I will focus on those that apply to several major fields: political science, marketing, economics, social services, and insurance. Statistics are so key to the nature of these fields that most of them could not exist without concepts such as the median and sampling. Political campaigns are designed to appeal to targeted demographics, which form the basis for blocks of voters. Whereas Abraham Lincoln wrote the Gettysburg address on the train to Pennsylvania on the back of an envelope, modern political speeches are designed to specifically appeal to a median group of voters, and to reflect the reasoning skills and personal tastes and values of these voters. A concept like the 'Axis of Evil,' seems adolescent to university professors and political analysts, but speech writers didn't have these people in mind when they created the concept; by definition, the median IQ is 100.…...

Statistical Data and Hypothesis Testing

Data AnalysisTo analyze this data, one must identify the variables and their types. The variables in this dataset are: Participant: Categorical (1 = yes, 0 = no) Extra-Curricular Involvement: Categorical (1 = yes, 0 = no) Residence: Categorical (On campus, Off campus, Parents) Motivation: Numerical (1-10) Life Satisfaction: Numerical (1-10) Exam1: Numerical (0-100) Exam2: Numerical (0-100) Exam3: Numerical (0-100)One can analyze this data using descriptive statistics and data visualization techniques to understand the relationships between variables. Here are some possible analyses that one can perform:1. Descriptive statistics for each variable: Participant: 8 participants (53.3%) are not involved in the program, and 7 participants (46.7%) are involved. Extra-Curricular Involvement: 7 participants (46.7%) are involved in extra-curricular activities, and 8 participants (53.3%) are not involved. Residence: 5 participants (33.3%) live on campus, 4 participants (26.7%) live off campus, and 6 participants (40%) live with their parents. Motivation: The mean motivation score is…...

Data Input Printed Questionnaires Manual Data Input

Data Input Printed Questionnaires. Manual data input method is appropriate for printed questionnaires. Since questionnaires are printed and therefore can be accessed as a hardcopy, the only way to input data on it is through manual writing. If the data will be transferred into a database, the appropriate method of data input is through data entry. Data entry on a computer is the appropriate method for this situation. For instance, while a surveyor is communicating with an interview over the phone, a computer in front of him can help him take note of the information from the telephone survey. Bank Check. Data entry to a database or bar code are the appropriate methods for this situation. Bank Check information can be keyed into a database or through scanning of the bank check's bar code. etail Tags. Bar code is the most appropriate method of data input from a retail tag. A bar code…...

mla References How Important Are Computer Clock Speed? Retrieved on November 2, 2005 from Online. Web site:   http://www.allbusiness.com/articles/StartingBusiness/817-25-1852.html  How Computer RAM Works.

Statistical Information the Role of

Another statistical measure that should be implemented is the use of statistical techniques to measure the side effects of certain drugs and medications given to patients. Possibly one of the most important statistical aspects that should be applied to modern nursing is the creation of clinical pathways in hospitals. The development of clinical pathways are related to "…attempts to reduce hospital utilization" and "cost-containment initiatives" ( Lagoe, 1998) There are many variables that have to be statistically considered in this regard and statistical analysis of data provides insight into the clinical pathway; for example, an analysis of the variables relating to the hospital population. While data and information collection processes are important, they are dependent on accurate and dependable analysis techniques to be effective and of use in nursing. While nursing is known as a profession that stresses qualitative aspects, there is an increasing emphasis on the accurate quantitative side of…...

mla References Giuliano K. And Polanowicz M. (2008) Interpretation and Use of Statistics in Nursing research: AACN advanced critical care (AACN Adv Crit Care), 19(2). Lagoe R. ( 1998) Basic statistics for clinical pathway evaluation. Nursing Economics, May-June, 1998. Retrieved April 9, 2009 from   http://findarticles.com/p/articles/mi_m0FSW/is_n3_v16/ai_n18607850/  Maindonald J. THIS PASSIONATE STUDY -- a DIALOGUE WITH FLORENCE NIGHTINGALE. Retrieved April

Statistical Methods

power of statistical analysis is the power to define, interpret, and understanding numerical data which represents patterns in the real world. Without the ability to measure statistical data, the empirical, hypothetical world of educational models would not be able to be checked by actual performance in the absolute. While statistics has applications in many fields, statistical data is possibly the most powerful when used to identify patterns in personal behavior, and other fields of study which do not exhibit direct patterns across a sampling group. For example, mathematical equations govern how a specific metal will respond to different loads, and different conditions. However, there are no direct mathematical equations which govern the percentage of teenage drivers who will be involved in traffic accidents over a period of time. In order to interpret the influential factors over teen drivers, a statistical measurement of actual experience can be undertaken. Through statistical…...

mla Regarding a linear regression analysis of this relationship, we find that the slope of the line is close to 0.5, and the relationship is a direct linear relationship between the amount of tar in a cigarette and the amount of nicotine. Nonlinear trends in statistical data can be the most challenging to work with. When non-linear relationships exist, there may be a mathematical relationship which is based on a logarithm, or other multi-factor influence. However, true non-linear relationship, such as the height and weight of a specific person who shops in a given department store may leave the statistician without any relationship whatsoever. Non-linear data can also be the result of data which is being acted on by an artificial, outside force. In this case, the statistician is able to verify the existence of an outside force, and then approach the process of identifying the force. An example of this situation is the expected relationship between supply and demand, and company profit based on the sales of a given product in the market place. In the early 1980's, the Coleco company produces a product called "Cabbage Patch dolls." The typical lifecycle of a new toy product is one to two years, but Coleco was able to extend the life of their product for four to five Christmas seasons by artificially affecting the relationship between supply and demand. The company had the production capacity to produce 4-5 times the amount of dolls which it shipped to the market during the first three years of the dolls life cycle. This would have produced a typical bell shaped curve, plotting a rising demand, and increasing profits which gave way to a declining demand and declining profits in a short period. However the company did not produce product equal to their capacity, nor equal to the demand. As a result, the company was able to continue a high level of demand, and an inflated retail based on the high demand for an extended period. The result was that the doll stayed popular for almost a decade, and the company was able to reap ongoing higher levels of profits. The longer bell curve, identified by an irregular and nonlinear relation between time and supply and demand was created by the unique marketing strategy for the company.

Statistical Project

Statistical Research A study performed by Sarah Kang and Lorenzo M. Polvani from the Columbia University claims the Earth's ozone layer hole has affected atmospheric circulation in the Southern hemisphere all the way to the equator, leading to increased rainfall in the subtropics (Kang, 2011). Previous work showed the ozone caused a dominant westerly jet stream in the mid-latitudes to move toward the pole with accompanying shifts in precipitation patterns. This study used different computerized climate models in the effort to identify the impact of the ozone depletion compared to other factors. The experiment found moistening in high latitudes, drying in mid-latitudes, and moistening in the subtropics. etween fifteen and thirty five degrees south, the researchers saw about a ten percent increase in precipitation. The depletion of the ozone layer, from 8 to 25 miles up, has caused severe cooling in the stratosphere, expanding to the troposphere, and altering in the…...

mla Bibliography Significant Ozone Hole Remains Over Antarctica. (2011, Oct 21). Retrieved from Science Daily:   http://www.sciencedaily.com/releases/2011/10/111020145106.htm  Kang, S. & . (2011, Apr 22). Study Links Ozone Hole to Weather Shifts. Retrieved from The Earth Institute Columbia University:   http://www.earth.columbia.edu/articles/view/2802  Karoly, D. (2012, Sep 14). The Antarctic ozone hole and climaste change: an anniversary worth celebrating. Retrieved from The Conversation:   http://theconversation.edu.au/the-antarctic-ozone-hole-and-climate-change-an-anniversary-worth-celebrating-9404  Ozone Hole Watch. (n.d.). Retrieved from NASA:   http://ozonewatch.gsfc.nasa.gov/meteorology/annual_data.html

Statistical Case Study The Possibility

The four possible points which could be the optimal solution are labeled from one to four. The solutions to these are then given in Table 1, along with the profits which would result from these combinations. The values of each of these points were calculated by solving the simultaneous equations where the lines crossed. It can be seen from Table 1 that the maximum profit would be reached by producing 20 beef dinners and 40 fish dinners each day. Figure 1: Feasible region for the linear programming problem Table 1: esultant profits from each of the critical points Point Value of X1 Value of X2 esultant Profit Now Excel may also be used to solve this problem. The solution which is given is shown in Figure 2. From this it may be confirmed that the optimal solution for the restaurant is to prepare 20 beef meals and 40 fish meals each night. The sensitivity report is…...

mla References Banker, R.D. & Morey, R.C. (1986). Efficiency analysis for exogenously fixed inputs and outputs. Operations Research, 34(4), 513-521. Brusco, M.J. & Johns, T.R. (1998). Staffing a multiskilled workforce with varying levels of productivity: An analysis of cross-training policies. Decision Sciences, 29(2), 499-515. Chase, R.B. & Apte, U.M. (2007). A history of research in service operations: What's the big idea? Journal of Operations Management, 25(2), 375-386. Gattoufi, S., Oral, M. & Reisman, a. (2004). A taxonomy for data envelopment analysis. Socio-Economic Planning Sciences, 38(2-3), 141-158.

Statistical vs Clinical Significance Statistical

In other words, p values correspond to statistical significance, while NNT corresponds to clinical significance. In clinical trials, statistical validity reflects the theoretical basis of the study, with hypotheses being formulated and quantified in terms of likelihood. Clinical significance is concerned with the practical outcome of trials, and with the results of actual treatment and how this relates to the hypotheses that are proven or void. 2. In nursing practice, both statistical and clinical significance play an important role in research. In practice, however, it is clinical significance that should have the greatest impact upon nursing practice. Clinical significance provides actual data from research conducted to determine such effects. It concerns the outcome of trials, while statistical significance is more concerned with determining new research and the likelihood of success before trials have been conducted. Indeed, Davidson notes that an advantage of NNT is the format of its results -- resulting from…...

mla References Davidson, Richard a. (1994) Does it Work or Not?: Clinical vs. Statistical Significance. Chest, Vol. 106, No. 3. Retrieved from http://chestjournal.chestpubs.org/content/106/3/932.long Kain, Z.N. (2005, Nov.) the Legend of the P. Value. Anesthesia & Analgesia, Vol. 101, No. 5. Retrieved from   http://www.anesthesia-analgesia.org/content/101/5/1454.full

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Statistical Analysis Essays

The impact of alphanumeric array on visual iconic memory recall, inferential statistics article critique, enhancing emergency department efficiency: the impact of a primary care clinic and telehealth call system on wait times, statistical analysis report, statistical analysis sas and r, popular essay topics.

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Introductory essay

Written by the educators who created Visualizing Data, a brief look at the key facts, tough questions and big ideas in their field. Begin this TED Study with a fascinating read that gives context and clarity to the material.

The reality of today

All of us now are being blasted by information design. It's being poured into our eyes through the Web, and we're all visualizers now; we're all demanding a visual aspect to our information...And if you're navigating a dense information jungle, coming across a beautiful graphic or a lovely data visualization, it's a relief, it's like coming across a clearing in the jungle. David McCandless

In today's complex 'information jungle,' David McCandless observes that "Data is the new soil." McCandless, a data journalist and information designer, celebrates data as a ubiquitous resource providing a fertile and creative medium from which new ideas and understanding can grow. McCandless's inspiration, statistician Hans Rosling, builds on this idea in his own TEDTalk with his compelling image of flowers growing out of data/soil. These 'flowers' represent the many insights that can be gleaned from effective visualization of data.

We're just learning how to till this soil and make sense of the mountains of data constantly being generated. As Gary King, Director of Harvard's Institute for Quantitative Social Science says in his New York Times article "The Age of Big Data":

It's a revolution. We're really just getting under way. But the march of quantification, made possible by enormous new sources of data, will sweep through academia, business and government. There is no area that is going to be untouched.

How do we deal with all this data without getting information overload? How do we use data to gain real insight into the world? Finding ways to pull interesting information out of data can be very rewarding, both personally and professionally. The managing editor of Financial Times observed on CNN's Your Money : "The people who are able to in a sophisticated and practical way analyze that data are going to have terrific jobs." Those who learn how to present data in effective ways will be valuable in every field.

Many people, when they think of data, think of tables filled with numbers. But this long-held notion is eroding. Today, we're generating streams of data that are often too complex to be presented in a simple "table." In his TEDTalk, Blaise Aguera y Arcas explores images as data, while Deb Roy uses audio, video, and the text messages in social media as data.

Some may also think that only a few specialized professionals can draw insights from data. When we look at data in the right way, however, the results can be fun, insightful, even whimsical — and accessible to everyone! Who knew, for example, that there are more relationship break-ups on Monday than on any other day of the week, or that the most break-ups (at least those discussed on Facebook) occur in mid-December? David McCandless discovered this by analyzing thousands of Facebook status updates.

Data, data, everywhere

There is more data available to us now than we can possibly process. Every minute , Internet users add the following to the big data pool (i):

• 204,166,667 email messages sent
• More than 2,000,000 Google searches
• 684,478 pieces of content added on Facebook
• $272,070 spent by consumers via online shopping
• More than 100,000 tweets on Twitter
• 47,000 app downloads from Apple
• 34,722 "likes" on Facebook for different brands and organizations
• 27,778 new posts on Tumblr blogs
• 3,600 new photos on Instagram
• 3,125 new photos on Flickr
• 2,083 check-ins on Foursquare
• 571 new websites created
• 347 new blog posts published on Wordpress
• 217 new mobile web users
• 48 hours of new video on YouTube

These numbers are almost certainly higher now, as you read this. And this just describes a small piece of the data being generated and stored by humanity. We're all leaving data trails — not just on the Internet, but in everything we do. This includes reams of financial data (from credit cards, businesses, and Wall Street), demographic data on the world's populations, meteorological data on weather and the environment, retail sales data that records everything we buy, nutritional data on food and restaurants, sports data of all types, and so on.

Governments are using data to search for terrorist plots, retailers are using it to maximize marketing strategies, and health organizations are using it to track outbreaks of the flu. But did you ever think of collecting data on every minute of your child's life? That's precisely what Deb Roy did. He recorded 90,000 hours of video and 140,000 hours of audio during his son's first years. That's a lot of data! He and his colleagues are using the data to understand how children learn language, and they're now extending this work to analyze publicly available conversations on social media, allowing them to take "the real-time pulse of a nation."

Data can provide us with new and deeper insight into our world. It can help break stereotypes and build understanding. But the sheer quantity of data, even in just any one small area of interest, is overwhelming. How can we make sense of some of this data in an insightful way?

The power of visualizing data

Visualization can help transform these mountains of data into meaningful information. In his TEDTalk, David McCandless comments that the sense of sight has by far the fastest and biggest bandwidth of any of the five senses. Indeed, about 80% of the information we take in is by eye. Data that seems impenetrable can come alive if presented well in a picture, graph, or even a movie. Hans Rosling tells us that "Students get very excited — and policy-makers and the corporate sector — when they can see the data."

It makes sense that, if we can effectively display data visually, we can make it accessible and understandable to more people. Should we worry, however, that by condensing data into a graph, we are simplifying too much and losing some of the important features of the data? Let's look at a fascinating study conducted by researchers Emre Soyer and Robin Hogarth . The study was conducted on economists, who are certainly no strangers to statistical analysis. Three groups of economists were asked the same question concerning a dataset:

• One group was given the data and a standard statistical analysis of the data; 72% of these economists got the answer wrong.
• Another group was given the data, the statistical analysis, and a graph; still 61% of these economists got the answer wrong.
• A third group was given only the graph, and only 3% got the answer wrong.

Visualizing data can sometimes be less misleading than using the raw numbers and statistics!

What about all the rest of us, who may not be professional economists or statisticians? Nathalie Miebach finds that making art out of data allows people an alternative entry into science. She transforms mountains of weather data into tactile physical structures and musical scores, adding both touch and hearing to the sense of sight to build even greater understanding of data.

Another artist, Chris Jordan, is concerned about our ability to comprehend big numbers. As citizens of an ever-more connected global world, we have an increased need to get useable information from big data — big in terms of the volume of numbers as well as their size. Jordan's art is designed to help us process such numbers, especially numbers that relate to issues of addiction and waste. For example, Jordan notes that the United States has the largest percentage of its population in prison of any country on earth: 2.3 million people in prison in the United States in 2005 and the number continues to rise. Jordan uses art, in this case a super-sized image of 2.3 million prison jumpsuits, to help us see that number and to help us begin to process the societal implications of that single data value. Because our brains can't truly process such a large number, his artwork makes it real.

The role of technology in visualizing data

The TEDTalks in this collection depend to varying degrees on sophisticated technology to gather, store, process, and display data. Handling massive amounts of data (e.g., David McCandless tracking 10,000 changes in Facebook status, Blaise Aguera y Arcas synching thousands of online images of the Notre Dame Cathedral, or Deb Roy searching for individual words in 90,000 hours of video tape) requires cutting-edge computing tools that have been developed specifically to address the challenges of big data. The ability to manipulate color, size, location, motion, and sound to discover and display important features of data in a way that makes it readily accessible to ordinary humans is a challenging task that depends heavily on increasingly sophisticated technology.

The importance of good visualization

There are good ways and bad ways of presenting data. Many examples of outstanding presentations of data are shown in the TEDTalks. However, sometimes visualizations of data can be ineffective or downright misleading. For example, an inappropriate scale might make a relatively small difference look much more substantial than it should be, or an overly complicated display might obfuscate the main relationships in the data. Statistician Kaiser Fung's blog Junk Charts offers many examples of poor representations of data (and some good ones) with descriptions to help the reader understand what makes a graph effective or ineffective. For more examples of both good and bad representations of data, see data visualization architect Andy Kirk's blog at visualisingdata.com . Both consistently have very current examples from up-to-date sources and events.

Creativity, even artistic ability, helps us see data in new ways. Magic happens when interesting data meets effective design: when statistician meets designer (sometimes within the same person). We are fortunate to live in a time when interactive and animated graphs are becoming commonplace, and these tools can be incredibly powerful. Other times, simpler graphs might be more effective. The key is to present data in a way that is visually appealing while allowing the data to speak for itself.

Changing perceptions through data

While graphs and charts can lead to misunderstandings, there is ultimately "truth in numbers." As Steven Levitt and Stephen Dubner say in Freakonomics , "[T]eachers and criminals and real-estate agents may lie, and politicians, and even C.I.A. analysts. But numbers don't." Indeed, consideration of data can often be the easiest way to glean objective insights. Again from Freakonomics : "There is nothing like the sheer power of numbers to scrub away layers of confusion and contradiction."

Data can help us understand the world as it is, not as we believe it to be. As Hans Rosling demonstrates, it's often not ignorance but our preconceived ideas that get in the way of understanding the world as it is. Publicly-available statistics can reshape our world view: Rosling encourages us to "let the dataset change your mindset."

Chris Jordan's powerful images of waste and addiction make us face, rather than deny, the facts. It's easy to hear and then ignore that we use and discard 1 million plastic cups every 6 hours on airline flights alone. When we're confronted with his powerful image, we engage with that fact on an entirely different level (and may never see airline plastic cups in the same way again).

The ability to see data expands our perceptions of the world in ways that we're just beginning to understand. Computer simulations allow us to see how diseases spread, how forest fires might be contained, how terror networks communicate. We gain understanding of these things in ways that were unimaginable only a few decades ago. When Blaise Aguera y Arcas demonstrates Photosynth, we feel as if we're looking at the future. By linking together user-contributed digital images culled from all over the Internet, he creates navigable "immensely rich virtual models of every interesting part of the earth" created from the collective memory of all of us. Deb Roy does somewhat the same thing with language, pulling in publicly available social media feeds to analyze national and global conversation trends.

Roy sums it up with these powerful words: "What's emerging is an ability to see new social structures and dynamics that have previously not been seen. ...The implications here are profound, whether it's for science, for commerce, for government, or perhaps most of all, for us as individuals."

Let's begin with the TEDTalk from David McCandless, a self-described "data detective" who describes how to highlight hidden patterns in data through its artful representation.

David McCandless

The beauty of data visualization.

i. Data obtained June 2012 from “How Much Data Is Created Every Minute?” on http://mashable.com/2012/06/22/data-created-every-minute/.

Relevant talks

Blaise Agüera y Arcas

How photosynth can connect the world's images.

Chris Jordan

Turning powerful stats into art.

The birth of a word

Hans Rosling

The magic washing machine.

Nathalie Miebach

Art made of storms.

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• Knowledge Base
• Choosing the Right Statistical Test | Types & Examples

Choosing the Right Statistical Test | Types & Examples

Published on January 28, 2020 by Rebecca Bevans . Revised on June 22, 2023.

Statistical tests are used in hypothesis testing . They can be used to:

• determine whether a predictor variable has a statistically significant relationship with an outcome variable.
• estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If you already know what types of variables you’re dealing with, you can use the flowchart to choose the right statistical test for your data.

Statistical tests flowchart

Table of contents

What does a statistical test do, when to perform a statistical test, choosing a parametric test: regression, comparison, or correlation, choosing a nonparametric test, flowchart: choosing a statistical test, other interesting articles, frequently asked questions about statistical tests.

Statistical tests work by calculating a test statistic – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship.

It then calculates a p value (probability value). The p -value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.

If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer no statistically significant relationship between the predictor and outcome variables.

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You can perform statistical tests on data that have been collected in a statistically valid manner – either through an experiment , or through observations made using probability sampling methods .

For a statistical test to be valid , your sample size needs to be large enough to approximate the true distribution of the population being studied.

To determine which statistical test to use, you need to know:

• whether your data meets certain assumptions.
• the types of variables that you’re dealing with.

Statistical assumptions

Statistical tests make some common assumptions about the data they are testing:

• Independence of observations (a.k.a. no autocorrelation): The observations/variables you include in your test are not related (for example, multiple measurements of a single test subject are not independent, while measurements of multiple different test subjects are independent).
• Homogeneity of variance : the variance within each group being compared is similar among all groups. If one group has much more variation than others, it will limit the test’s effectiveness.
• Normality of data : the data follows a normal distribution (a.k.a. a bell curve). This assumption applies only to quantitative data .

If your data do not meet the assumptions of normality or homogeneity of variance, you may be able to perform a nonparametric statistical test , which allows you to make comparisons without any assumptions about the data distribution.

If your data do not meet the assumption of independence of observations, you may be able to use a test that accounts for structure in your data (repeated-measures tests or tests that include blocking variables).

Types of variables

The types of variables you have usually determine what type of statistical test you can use.

Quantitative variables represent amounts of things (e.g. the number of trees in a forest). Types of quantitative variables include:

• Continuous (aka ratio variables): represent measures and can usually be divided into units smaller than one (e.g. 0.75 grams).
• Discrete (aka integer variables): represent counts and usually can’t be divided into units smaller than one (e.g. 1 tree).

Categorical variables represent groupings of things (e.g. the different tree species in a forest). Types of categorical variables include:

• Ordinal : represent data with an order (e.g. rankings).
• Nominal : represent group names (e.g. brands or species names).
• Binary : represent data with a yes/no or 1/0 outcome (e.g. win or lose).

Choose the test that fits the types of predictor and outcome variables you have collected (if you are doing an experiment , these are the independent and dependent variables ). Consult the tables below to see which test best matches your variables.

Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests.

The most common types of parametric test include regression tests, comparison tests, and correlation tests.

Regression tests

Regression tests look for cause-and-effect relationships . They can be used to estimate the effect of one or more continuous variables on another variable.

Comparison tests

Comparison tests look for differences among group means . They can be used to test the effect of a categorical variable on the mean value of some other characteristic.

T-tests are used when comparing the means of precisely two groups (e.g., the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g., the average heights of children, teenagers, and adults).

Correlation tests

Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship.

These can be used to test whether two variables you want to use in (for example) a multiple regression test are autocorrelated.

Non-parametric tests don’t make as many assumptions about the data, and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests.

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This flowchart helps you choose among parametric tests. For nonparametric alternatives, check the table above.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient
• Null hypothesis

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Statistical tests commonly assume that:

• the data are normally distributed
• the groups that are being compared have similar variance
• the data are independent

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

A test statistic is a number calculated by a  statistical test . It describes how far your observed data is from the  null hypothesis  of no relationship between  variables or no difference among sample groups.

The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis . Different test statistics are used in different statistical tests.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

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The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organisations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organise and summarise the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalise your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarise your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, frequently asked questions about statistics.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

• Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
• Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
• Null hypothesis: Parental income and GPA have no relationship with each other in college students.
• Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

• In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
• In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
• In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

• In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
• In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
• In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
• Experimental
• Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalise your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

• Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
• Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

• Probability sampling: every member of the population has a chance of being selected for the study through random selection.
• Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalisable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

• your sample is representative of the population you’re generalising your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalise your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialised, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalised in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

• Will you have resources to advertise your study widely, including outside of your university setting?
• Will you have the means to recruit a diverse sample that represents a broad population?
• Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

• Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
• Expected effect size : a standardised indication of how large the expected result of your study will be, usually based on other similar studies.
• Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarise them.

Inspect your data

There are various ways to inspect your data, including the following:

• Organising data from each variable in frequency distribution tables .
• Displaying data from a key variable in a bar chart to view the distribution of responses.
• Visualising the relationship between two variables using a scatter plot .

By visualising your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

• Mode : the most popular response or value in the data set.
• Median : the value in the exact middle of the data set when ordered from low to high.
• Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

• Range : the highest value minus the lowest value of the data set.
• Interquartile range : the range of the middle half of the data set.
• Standard deviation : the average distance between each value in your data set and the mean.
• Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

• Estimation: calculating population parameters based on sample statistics.
• Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

• A point estimate : a value that represents your best guess of the exact parameter.
• An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

• A test statistic tells you how much your data differs from the null hypothesis of the test.
• A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

• Comparison tests assess group differences in outcomes.
• Regression tests assess cause-and-effect relationships between variables.
• Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

• A simple linear regression includes one predictor variable and one outcome variable.
• A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

• A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
• A z test is for exactly 1 or 2 groups when the sample is large.
• An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

• If you have only one sample that you want to compare to a population mean, use a one-sample test .
• If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
• If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
• If you expect a difference between groups in a specific direction, use a one-tailed test .
• If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

• a t value (test statistic) of 3.00
• a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

• a t value of 3.08
• a p value of 0.001

The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimise the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasises null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
• If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Statistical analysis is the main method for analyzing quantitative research data . It uses probabilities and models to test predictions about a population from sample data.

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Business Data and Statistical Analysis Essay

• To find inspiration for your paper and overcome writer’s block
• As a source of information (ensure proper referencing)
• As a template for you assignment

Profitability is one of the inherent components of any profit-making business. To achieve this, a business requires the use of promotion and advertising strategies to market its product. A study was carried out in the United States to determine the frequency and benefits of advertising and promotion strategies that were being used by restaurants in the urban center. The study concentrated on ten major advertising and promotion strategies that were believed to be used frequently. Out of the total number of restaurants in the urban areas, only 88 were surveyed (n=88). This was a very small sample size compared to the total number of restaurants in the area. Often a bigger sample size results in precise estimates as compared to the small size. However, as the sample size becomes very large, the variability of data becomes small (Jackson, et al 2010).

The respondents were surveyed by use of phone because it was one of the resalable sources. Statistics show that more than 270 million people are mobile phone subscribers representing 87% of the total population in the United States. It was reviewed that more than one trillion people sent or received text messages every year. The choice to use mobile phones was well thought because it was deemed to reach a big population of the selected sample size. The respondents of the study were required to evaluate the strategies used based on their derived benefits and frequency. However, the study achieved only a 39.7% response rate (Jackson, et al 2010). This was not a good response rate considering the total population in the urban centers and that these restaurants were the main source of food for over 50% of the population. It was found that there was limited use of the promotion and advertising strategies and many people relied on the phone coupons. It was further noted that the use of radio, the internet, and food samples also seemed to be frequently used.

As a marketing manager, it is good to note that sampling is used by statisticians to derive conclusions about a big population by studying a part of it. It is one of the techniques that enable a business to approximate the characteristics of a given population by studying a part of the total population. What we are usually interested in is not the sample itself, but what can be gained from the study and how the collected data can be applied to the total population. The sample size selected should be able to represent the entire population and be responsible for giving about a 95% response rate. High response rates are critical to the success of surveys because the potential for no response bias increases as the response rate decreases. The response rate is the ratio of the number of units with completed interviews (for example telephone numbers) to the number of units sampled and eligible to complete the interview (Bragg, 2009).

The sample survey should be clear and well organized with the right questions asked to the right people. From my understanding, I think that, the above survey was not well organized and that questions were directed to the wrong people thus the poor rate in response. If I was to carry out a survey today, the first step would be to spell out the objectives with much detail as possible. For example, in the article discussed above, the objectives were clear since they were aimed at investigating the frequency and benefits of ten advertising and promotion strategies. I would then decide on the data requirements and the data collection technique. This technique must be sound and able to give enough information. The selection of a phone survey was a good technique considering the level of technology and the unavailability of people for face-to-face surveys. For our business, I would choose the use of phone or internet because most of our customers are of high technology and at the same time they are very busy for face to face interaction. The level of certainty or precision of data depends on the size and composition of the selected sample.

Statistical surveys are important because sometimes the data needed for a particular application are not available through existing sources. In such cases, the data can often be obtained by conducting a statistical study. This can either be an experimental study or an observational study (Anderson, et al 2008). Thereafter one or more other variables are taken for control after which data on their influence is acquired. For example in our restaurant, we might be interested in experimenting to learn about how a new brand of food would affect the health of our customers.

As a manager, I have learned that when using data and statistical analysis as aids to decision making I must be aware of the time and cost required to obtain the data. The use of existing data sources is sought-after when data must be obtained in a relatively short period. The cost of data acquirement and the subsequent statistical analysis should not exceed the savings generated by using the information to make a better decision.

Reference List

• Anderson, D. R., et al (2008). Fundamentals of Business Statistics . New York: Cengage Learning EMEA
• Bragg, S. M. (2009). Wiley Practitioner’s Guide to GAAS 2010: Covering All SASs, SSAEs, SSARSs, and Interpretations Wiley practitioner’s guide to GAAS . New York: John Wiley and Sons
• Jackson, F. H. et al (2010). Frequency of Restaurant advertising and promotion strategies: Exploring an urban market .
• Exemplary Business Research Problem Identification
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IvyPanda. (2021, December 27). Business Data and Statistical Analysis. https://ivypanda.com/essays/statistical-application/

"Business Data and Statistical Analysis." IvyPanda , 27 Dec. 2021, ivypanda.com/essays/statistical-application/.

IvyPanda . (2021) 'Business Data and Statistical Analysis'. 27 December.

IvyPanda . 2021. "Business Data and Statistical Analysis." December 27, 2021. https://ivypanda.com/essays/statistical-application/.

1. IvyPanda . "Business Data and Statistical Analysis." December 27, 2021. https://ivypanda.com/essays/statistical-application/.

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Statistical Analysis Using SPSS, Essay Example

Pages: 3

Words: 830

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Use the dataset provided on Blackboard to conduct a statistical analysis of the relationship between two variables of your choice. CHOOSE one variable to be your “cause” (independent variable) and one to be your “effect” (dependent variable). Model your analyses after the in-class demonstration.

Please ANSWER the following questions about your analysis. Your answers should total at least 1½ pages in length, including your table. Please remember to follow the other formatting guidelines set forth in the syllabus.

What are the mean, range (or minimum and maximum), and standard deviation of your independent variable?

In this analysis, I am examining the times used marijuana in public (independent variable) on importance of college to respondent (dependent variable).  The mean for the independent variable is 1.79; the minimum value is 1- the maximum value is 3.  The standard deviation is .811.

Please write a sentence interpreting the mean you computed for question 1. That is, tell me what this number means in words (e.g., tell me how old the respondents are on average, the percentage of respondents who are male, how important the average respondent feels college is, or whatever is appropriate for your variable). To do this you will probably need to examine the value labels.

The independent variable is a scaled variable: the mean could be interpreted as the average respondent in this survey has marijuana at least once.  The interpretation of this variable is complicated by the fact that it is not a continuous variable- thus the scale must interpreted to the “average” individual.

What are the mean, range (or minimum and maximum), and standard deviation of your dependent variable?

The mean for the importance of college is 3.94.  The minimum was 1; the maximum was 5.  The standard deviation was 1.428.

Present a contingency table for your chosen variables. If the table that SPSS gives you is cluttered or difficult to read you should retype it. Be sure to place the independent and dependent variables in the correct places. Clearly label the rows and columns and include an informative title for your table. Do not simply copy the table title that SPSS gives you. Write a better one (see Chapter 11 for examples).

Individuals who have smoked Marijuana more than once (generally) hold the opinion that college is less important compared to individuals that have not smoked Marijuana who (generally) hold the opinion that college is more important.

Describe the relationship between your two variables. What pattern, if any, do you see in your table?

There is not a particularly discernible pattern to the data, but it would seem that those who have never done marijuana give a higher importance to college; those who have done marijuana more than once give a lower importance to college.

State the null hypothesis for your chi square analysis.

The null hypothesis is that there is not a correlation between the times used marijuana (independent variable) and importance of college to the respondent (dependent variable).

State your chi square results (use the Pearson Chi-Square given in the SPSS output). Is your relationship statistically significant? If so, at what level?

There is a negative correlation between the two variables.  That is with an increase in times used marijuana, there is a decrease in the importance of college to the respondent.  Although the negative correlation is not necessarily robust (-.217); the relationship is significant at the .001 level.

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