greater than (>) less than (<)
H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30
H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.
H 0 : The drug reduces cholesterol by 25%. p = 0.25
H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:
H 0 : μ = 2.0
H a : μ ≠ 2.0
We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66
We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
H 0 : μ ≥ 5
H a : μ < 5
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45
In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
H 0 : p ≤ 0.066
H a : p > 0.066
On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40
In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.
H 0 and H a are contradictory.
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One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter.
Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealership advertises that its new small truck gets 35 miles per gallon on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that female managers in their company earn an average of $60,000 per year. A statistician may want to make a decision about or evaluate these claims. A hypothesis test can be used to do this.
A hypothesis test involves collecting data from a sample and evaluating the data. Then the statistician makes a decision as to whether or not there is sufficient evidence to reject the null hypothesis based upon analyses of the data.
In this section, you will conduct hypothesis tests on single means when the population standard deviation is known.
Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will perform some variation of these steps:
The actual test begins by considering two hypotheses: the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.
The null hypothesis ( H 0 ) is often a statement of the accepted historical value or norm. This is your starting point that you must assume from the beginning in order to show an effect exists.
The alternative hypothesis ( H a ) is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .
Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.
After you have determined which hypothesis the sample supports, you make a decision . There are two options for a decision. They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.
The following table shows mathematical symbols used in H 0 and H a :
equal (=) | not equal (≠) greater than (>) less than (<) |
equal (=) | less than (<) |
equal (=) | more than (>) |
NOTE: H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol in the alternative hypothesis depends on the wording of the hypothesis test. Despite this, many researchers may use =, ≤, or ≥ in the null hypothesis. This practice is acceptable because our only decision is to reject or not reject the null hypothesis.
We want to test whether the mean GPA of students in American colleges is 2.0 (out of 4.0). The null hypothesis is: H 0 : μ = 2.0. What is the alternative hypothesis?
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.
Once you have defined your hypotheses, the next step in the process is to collect sample data. In a classroom context, the data or summary statistics will usually be given to you.
Then you will have to determine the correct distribution to perform the hypothesis test, given the assumptions you are able to make about the situation. Right now, we are demonstrating these ideas in a test for a mean when the population standard deviation is known using the z distribution. We will see other scenarios in the future.
Next you will start evaluating the data. This begins with calculating your test statistic , which is a measure of the distance between what you observed and what you are assuming to be true. In this context, your test statistic, z ο , quantifies the number of standard deviations between the sample mean, x, and the population mean, µ . Calculating the test statistic is analogous to the previously discussed process of standardizing observations with z -scores:
where µ o is the value assumed to be true in the null hypothesis.
Once you have your test statistic, there are two methods to use it to make your decision:
To find a p -value , we use the test statistic to calculate the actual probability of getting the test result. Formally, the p -value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.
A large p -value calculated from the data indicates that we should not reject the null hypothesis. The smaller the p -value, the more unlikely the outcome and the stronger the evidence is against the null hypothesis. We would reject the null hypothesis if the evidence is strongly against it.
Draw a graph that shows the p -value. The hypothesis test is easier to perform if you use a graph because you see the problem more clearly.
Suppose a baker claims that his bread height is more than 15 cm on average. Several of his customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes ten loaves of bread. The mean height of the sample loaves is 17 cm. The baker knows from baking hundreds of loaves of bread that the standard deviation for the height is 0.5 cm and the distribution of heights is normal.
The null hypothesis could be H 0 : μ ≤ 15.
The alternate hypothesis is H a : μ > 15.
The words “is more than” calls for the use of the > symbol, so “ μ > 15″ goes into the alternate hypothesis. The null hypothesis must contradict the alternate hypothesis.
Suppose the null hypothesis is true (the mean height of the loaves is no more than 15 cm). Then, is the mean height (17 cm) calculated from the sample unexpectedly large? The hypothesis test works by asking how unlikely the sample mean would be if the null hypothesis were true. The graph shows how far out the sample mean is on the normal curve. The p -value is the probability that, if we were to take other samples, any other sample mean would fall at least as far out as 17 cm.
This means that the p -value is the probability that a sample mean is the same or greater than 17 cm when the population mean is, in fact, 15 cm. We can calculate this probability using the normal distribution for means.
A p -value of approximately zero tells us that it is highly unlikely that a loaf of bread rises no more than 15 cm on average. That is, almost 0% of all loaves of bread would be at least as high as 17 cm purely by CHANCE had the population mean height really been 15 cm. Because the outcome of 17 cm is so unlikely (meaning it is happening NOT by chance alone), we conclude that the evidence is strongly against the null hypothesis that the mean height would be at most 15 cm. There is sufficient evidence that the true mean height for the population of the baker’s loaves of bread is greater than 15 cm.
A normal distribution has a standard deviation of one. We want to verify a claim that the mean is greater than 12. A sample of 36 is taken with a sample mean of 12.5.
Find the p -value.
A systematic way to decide whether to reject or not reject the null hypothesis is to compare the p -value and a preset or preconceived α (also called a significance level ). A preset α is the probability of a type I error (rejecting the null hypothesis when the null hypothesis is true). It may or may not be given to you at the beginning of the problem. If there is no given preconceived α , then use α = 0.05.
When you make a decision to reject or not reject H 0 , do as follows:
After you make your decision, write a thoughtful conclusion in the context of the scenario incorporating the hypotheses.
NOTE: When you “do not reject H 0 ,” it does not mean that you should believe that H 0 is true. It simply means that the sample data have failed to provide sufficient evidence to cast serious doubt about the truthfulness of H o .
When using the p -value to evaluate a hypothesis test, the following rhymes can come in handy:
If the p -value is low, the null must go.
If the p -value is high, the null must fly.
This memory aid relates a p -value less than the established alpha (“the p -value is low”) as rejecting the null hypothesis and, likewise, relates a p -value higher than the established alpha (“the p -value is high”) as not rejecting the null hypothesis.
Fill in the blanks:
It’s a Boy Genetics Labs claim their procedures improve the chances of a boy being born. The results for a test of a single population proportion are as follows:
Interpret the results and state a conclusion in simple, non-technical terms.
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Figure References
Figure 5.11: Alora Griffiths (2019). dalmatian puppy near man in blue shorts kneeling. Unsplash license. https://unsplash.com/photos/7aRQZtLsvqw
Figure 5.13: Kindred Grey (2020). Bread height probability. CC BY-SA 4.0.
A decision-making procedure for determining whether sample evidence supports a hypothesis
The claim that is assumed to be true and is tested in a hypothesis test
A working hypothesis that is contradictory to the null hypothesis
A measure of the difference between observations and the hypothesized (or claimed) value
The probability that an event will occur, assuming the null hypothesis is true
Probability that a true null hypothesis will be rejected, also known as type I error and denoted by α
Finding sufficient evidence that the observed effect is not just due to variability, often from rejecting the null hypothesis
Significant Statistics Copyright © 2024 by John Morgan Russell, OpenStaxCollege, OpenIntro is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.
In mathematics, Statistics deals with the study of research and surveys on the numerical data. For taking surveys, we have to define the hypothesis. Generally, there are two types of hypothesis. One is a null hypothesis, and another is an alternative hypothesis .
In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening. For example, there is no connection among groups or no association between two measured events. It is generally assumed here that the hypothesis is true until any other proof has been brought into the light to deny the hypothesis. Let us learn more here with definition, symbol, principle, types and example, in this article.
Table of contents:
The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given population or sample . In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance. It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H 0 .
In statistics, the null hypothesis is usually denoted by letter H with subscript ‘0’ (zero), such that H 0 . It is pronounced as H-null or H-zero or H-nought. At the same time, the alternative hypothesis expresses the observations determined by the non-random cause. It is represented by H 1 or H a .
The principle followed for null hypothesis testing is, collecting the data and determining the chances of a given set of data during the study on some random sample, assuming that the null hypothesis is true. In case if the given data does not face the expected null hypothesis, then the outcome will be quite weaker, and they conclude by saying that the given set of data does not provide strong evidence against the null hypothesis because of insufficient evidence. Finally, the researchers tend to reject that.
Here, the hypothesis test formulas are given below for reference.
The formula for the null hypothesis is:
H 0 : p = p 0
The formula for the alternative hypothesis is:
H a = p >p 0 , < p 0 ≠ p 0
The formula for the test static is:
Remember that, p 0 is the null hypothesis and p – hat is the sample proportion.
Also, read:
There are different types of hypothesis. They are:
Simple Hypothesis
It completely specifies the population distribution. In this method, the sampling distribution is the function of the sample size.
Composite Hypothesis
The composite hypothesis is one that does not completely specify the population distribution.
Exact Hypothesis
Exact hypothesis defines the exact value of the parameter. For example μ= 50
Inexact Hypothesis
This type of hypothesis does not define the exact value of the parameter. But it denotes a specific range or interval. For example 45< μ <60
Sometimes the null hypothesis is rejected too. If this hypothesis is rejected means, that research could be invalid. Many researchers will neglect this hypothesis as it is merely opposite to the alternate hypothesis. It is a better practice to create a hypothesis and test it. The goal of researchers is not to reject the hypothesis. But it is evident that a perfect statistical model is always associated with the failure to reject the null hypothesis.
The null hypothesis says there is no correlation between the measured event (the dependent variable) and the independent variable. We don’t have to believe that the null hypothesis is true to test it. On the contrast, you will possibly assume that there is a connection between a set of variables ( dependent and independent).
The null hypothesis is rejected using the P-value approach. If the P-value is less than or equal to the α, there should be a rejection of the null hypothesis in favour of the alternate hypothesis. In case, if P-value is greater than α, the null hypothesis is not rejected.
Now, let us discuss the difference between the null hypothesis and the alternative hypothesis.
|
| |
1 | The null hypothesis is a statement. There exists no relation between two variables | Alternative hypothesis a statement, there exists some relationship between two measured phenomenon |
2 | Denoted by H | Denoted by H |
3 | The observations of this hypothesis are the result of chance | The observations of this hypothesis are the result of real effect |
4 | The mathematical formulation of the null hypothesis is an equal sign | The mathematical formulation alternative hypothesis is an inequality sign such as greater than, less than, etc. |
Here, some of the examples of the null hypothesis are given below. Go through the below ones to understand the concept of the null hypothesis in a better way.
If a medicine reduces the risk of cardiac stroke, then the null hypothesis should be “the medicine does not reduce the chance of cardiac stroke”. This testing can be performed by the administration of a drug to a certain group of people in a controlled way. If the survey shows that there is a significant change in the people, then the hypothesis is rejected.
Few more examples are:
1). Are there is 100% chance of getting affected by dengue?
Ans: There could be chances of getting affected by dengue but not 100%.
2). Do teenagers are using mobile phones more than grown-ups to access the internet?
Ans: Age has no limit on using mobile phones to access the internet.
3). Does having apple daily will not cause fever?
Ans: Having apple daily does not assure of not having fever, but increases the immunity to fight against such diseases.
4). Do the children more good in doing mathematical calculations than grown-ups?
Ans: Age has no effect on Mathematical skills.
In many common applications, the choice of the null hypothesis is not automated, but the testing and calculations may be automated. Also, the choice of the null hypothesis is completely based on previous experiences and inconsistent advice. The choice can be more complicated and based on the variety of applications and the diversity of the objectives.
The main limitation for the choice of the null hypothesis is that the hypothesis suggested by the data is based on the reasoning which proves nothing. It means that if some hypothesis provides a summary of the data set, then there would be no value in the testing of the hypothesis on the particular set of data.
What is meant by the null hypothesis.
In Statistics, a null hypothesis is a type of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.
Hypothesis testing is defined as a form of inferential statistics, which allows making conclusions from the entire population based on the sample representative.
The null hypothesis is either accepted or rejected in terms of the given data. If P-value is less than α, then the null hypothesis is rejected in favor of the alternative hypothesis, and if the P-value is greater than α, then the null hypothesis is accepted in favor of the alternative hypothesis.
The importance of the null hypothesis is that it provides an approximate description of the phenomena of the given data. It allows the investigators to directly test the relational statement in a research study.
If the result of the chi-square test is bigger than the critical value in the table, then the data does not fit the model, which represents the rejection of the null hypothesis.
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Making a certain class or laboratory experiment would require a good null hypothesis . You will be given variables to be used in your experiment and then you would be able to identify the relationship between the two. Every beginning of the experiment report would indicate your hypotheses. It is proven useful for it can be tested to prove if the result is considered false.
A null hypothesis is used during experiments to prove that there is no difference in the relationship between the two variables. Every type of experiment would require you to make a null hypothesis. From the word itself “null” means zero or no value. If you want to practice making a good experiment report , consider providing a good null hypothesis. Null hypothesis is designed to be rejected if the alternative hypothesis is proven to be exact.
1. medical research.
1. effectiveness of therapy.
1. effect of fertilizers on plant growth.
1. effect of marketing campaign on sales.
1. comparing means.
1. medical studies.
1. null hypothesis significance test example.
The null hypothesis is a fundamental concept in statistics and scientific research . It serves several critical purposes in the process of hypothesis testing, guiding researchers in drawing meaningful conclusions from their data. Below are the primary purposes of the null hypothesis:
The null hypothesis provides a baseline or a default position that indicates no effect, no difference, or no relationship between variables. It is the statement that researchers aim to test against an alternative hypothesis. By starting with the assumption that there is no effect, researchers can objectively assess whether the data provide enough evidence to support the alternative hypothesis.
By assuming no effect or no difference, the null hypothesis helps eliminate bias in research. Researchers approach their study without preconceived notions about the outcome, ensuring that the results are based on the data collected rather than personal beliefs or expectations.
The null hypothesis provides a structured framework for conducting statistical tests. It is essential for calculating p-values and test statistics, which determine whether the observed data are significantly different from what would be expected under the null hypothesis. This framework allows for a standardized approach to testing hypotheses across various fields of study.
The null hypothesis facilitates decision-making in research by providing clear criteria for accepting or rejecting it. If the data provide sufficient evidence to reject the null hypothesis, researchers can conclude that there is a statistically significant effect or difference. This decision-making process is critical in advancing scientific knowledge and understanding.
The null hypothesis plays a crucial role in controlling Type I and Type II errors in hypothesis testing. A Type I error occurs when the null hypothesis is incorrectly rejected (a false positive), while a Type II error happens when the null hypothesis is incorrectly accepted (a false negative). By defining the null hypothesis, researchers can set significance levels (e.g., alpha level) to manage the risk of these errors.
Rejecting the null hypothesis is a critical step in the process of hypothesis testing. The decision to reject the null hypothesis is based on statistical evidence derived from the data collected in a study. Below are the key factors that determine when the null hypothesis is rejected:
The p-value is a measure of the probability that the observed data (or something more extreme) would occur if the null hypothesis were true. The null hypothesis is rejected if the p-value is less than or equal to the predetermined significance level (?).
The test statistic is a standardized value calculated from sample data during a hypothesis test. It measures the degree to which the sample data differ from the null hypothesis. The decision to reject the null hypothesis depends on whether the test statistic falls within the critical region.
Confidence intervals provide a range of values that are likely to contain the population parameter. If the confidence interval does not include the value specified by the null hypothesis, the null hypothesis is rejected.
Effect size measures the magnitude of the difference between groups or the strength of a relationship between variables. While not a direct criterion for rejecting the null hypothesis, a substantial effect size can support the decision to reject the null hypothesis when combined with a significant p-value.
A statement that there is no effect or difference. | A statement that there is an effect or difference. | |
Serves as a baseline or default position. | Represents the outcome the researcher aims to support. | |
Assumes no relationship or effect. | Assumes a relationship or effect exists. | |
“The new drug has no effect on blood pressure.” | “The new drug lowers blood pressure.” | |
Retained if the p-value is greater than the significance level (?). | Accepted if the p-value is less than or equal to the significance level (?). | |
Falls outside the critical region, indicating no significant effect. | Falls within the critical region, indicating a significant effect. | |
Denoted by H0. | Denoted by H1 or Ha. | |
Focuses on the absence of a significant effect or relationship. | Focuses on the presence of a significant effect or relationship. | |
Incorrectly rejecting a true null hypothesis (false positive). | N/A | |
N/A | Incorrectly accepting a false null hypothesis (false negative). |
Writing a null hypothesis is a crucial step in designing a scientific study or experiment. The null hypothesis (H0) serves as a starting point for statistical testing and represents a statement of no effect or no difference. Here’s a step-by-step guide on how to write a null hypothesis:
Start by clearly defining the research question you want to investigate. Understand what you are testing and what you expect to find.
Identify the independent and dependent variables in your study.
The null hypothesis should assert that there is no effect, no difference, or no relationship between the variables. It is usually written as a statement of equality or no change.
In formal scientific writing, use symbols and proper notation to represent the null hypothesis.
The null hypothesis is crucial as it provides a baseline for comparison and allows researchers to test the significance of their findings.
A null hypothesis is stated as no effect or no difference, typically in the form “There is no [effect/difference] between [groups/variables].”
The alternative hypothesis (H1) suggests that there is an effect or difference between variables, opposing the null hypothesis.
Rejecting the null hypothesis means the data provides sufficient evidence to support the alternative hypothesis, indicating a significant effect or difference.
A p-value measures the probability that the observed data would occur if the null hypothesis were true. Low p-values indicate strong evidence against the null hypothesis.
A Type I error occurs when the null hypothesis is incorrectly rejected, meaning a false positive result is concluded.
A Type II error happens when the null hypothesis is incorrectly accepted, meaning a false negative result is concluded.
The significance level, often set at 0.05, is chosen based on the acceptable risk of making a Type I error in the context of the study.
No, the null hypothesis can only be rejected or not rejected. Failing to reject it does not prove it true, only that there is not enough evidence against it.
Larger sample sizes increase the test’s power, reducing the risk of Type II errors and making it easier to detect a true effect.
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Published on January 7, 2021 by Pritha Bhandari . Revised on June 22, 2023.
If a result is statistically significant , that means it’s unlikely to be explained solely by chance or random factors. In other words, a statistically significant result has a very low chance of occurring if there were no true effect in a research study.
The p value , or probability value, tells you the statistical significance of a finding. In most studies, a p value of 0.05 or less is considered statistically significant, but this threshold can also be set higher or lower.
How do you test for statistical significance, what is a significance level, problems with relying on statistical significance, other types of significance in research, other interesting articles, frequently asked questions about statistical significance.
In quantitative research , data are analyzed through null hypothesis significance testing, or hypothesis testing. This is a formal procedure for assessing whether a relationship between variables or a difference between groups is statistically significant.
To begin, research predictions are rephrased into two main hypotheses: the null and alternative hypothesis .
Hypothesis testin g always starts with the assumption that the null hypothesis is true. Using this procedure, you can assess the likelihood (probability) of obtaining your results under this assumption. Based on the outcome of the test, you can reject or retain the null hypothesis.
Every statistical test produces:
The p value determines statistical significance. An extremely low p value indicates high statistical significance, while a high p value means low or no statistical significance.
Next, you perform a t test to see whether actively smiling leads to more happiness. Using the difference in average happiness between the two groups, you calculate:
The significance level , or alpha (α), is a value that the researcher sets in advance as the threshold for statistical significance. It is the maximum risk of making a false positive conclusion ( Type I error ) that you are willing to accept .
In a hypothesis test, the p value is compared to the significance level to decide whether to reject the null hypothesis.
Usually, the significance level is set to 0.05 or 5%. That means your results must have a 5% or lower chance of occurring under the null hypothesis to be considered statistically significant.
The significance level can be lowered for a more conservative test. That means an effect has to be larger to be considered statistically significant.
The significance level may also be set higher for significance testing in non-academic marketing or business contexts. This makes the study less rigorous and increases the probability of finding a statistically significant result.
As best practice, you should set a significance level before you begin your study. Otherwise, you can easily manipulate your results to match your research predictions.
It’s important to note that hypothesis testing can only show you whether or not to reject the null hypothesis in favor of the alternative hypothesis. It can never “prove” the null hypothesis, because the lack of a statistically significant effect doesn’t mean that absolutely no effect exists.
When reporting statistical significance, include relevant descriptive statistics about your data (e.g., means and standard deviations ) as well as the test statistic and p value.
There are various critiques of the concept of statistical significance and how it is used in research.
Researchers classify results as statistically significant or non-significant using a conventional threshold that lacks any theoretical or practical basis. This means that even a tiny 0.001 decrease in a p value can convert a research finding from statistically non-significant to significant with almost no real change in the effect.
On its own, statistical significance may also be misleading because it’s affected by sample size. In extremely large samples , you’re more likely to obtain statistically significant results, even if the effect is actually small or negligible in the real world. This means that small effects are often exaggerated if they meet the significance threshold, while interesting results are ignored when they fall short of meeting the threshold.
The strong emphasis on statistical significance has led to a serious publication bias and replication crisis in the social sciences and medicine over the last few decades. Results are usually only published in academic journals if they show statistically significant results—but statistically significant results often can’t be reproduced in high quality replication studies.
As a result, many scientists call for retiring statistical significance as a decision-making tool in favor of more nuanced approaches to interpreting results.
That’s why APA guidelines advise reporting not only p values but also effect sizes and confidence intervals wherever possible to show the real world implications of a research outcome.
Aside from statistical significance, clinical significance and practical significance are also important research outcomes.
Practical significance shows you whether the research outcome is important enough to be meaningful in the real world. It’s indicated by the effect size of the study.
Clinical significance is relevant for intervention and treatment studies. A treatment is considered clinically significant when it tangibly or substantially improves the lives of patients.
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.
Methodology
Research bias
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.
A p -value , or probability value, is a number describing how likely it is that your data would have occurred under the null hypothesis of your statistical test .
P -values are usually automatically calculated by the program you use to perform your statistical test. They can also be estimated using p -value tables for the relevant test statistic .
P -values are calculated from the null distribution of the test statistic. They tell you how often a test statistic is expected to occur under the null hypothesis of the statistical test, based on where it falls in the null distribution.
If the test statistic is far from the mean of the null distribution, then the p -value will be small, showing that the test statistic is not likely to have occurred under the null hypothesis.
No. The p -value only tells you how likely the data you have observed is to have occurred under the null hypothesis .
If the p -value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.
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Bhandari, P. (2023, June 22). An Easy Introduction to Statistical Significance (With Examples). Scribbr. Retrieved September 9, 2024, from https://www.scribbr.com/statistics/statistical-significance/
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How to Write a Null Hypothesis (5 Examples) A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true. Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H0 (Null Hypothesis): Population parameter =, ≤, ≥ ...
The null hypothesis (H0) answers "No, there's no effect in the population.". The alternative hypothesis (Ha) answers "Yes, there is an effect in the population.". The null and alternative are always claims about the population. That's because the goal of hypothesis testing is to make inferences about a population based on a sample.
The null hypothesis is among the easiest hypothesis to test using statistical analysis, making it perhaps the most valuable hypothesis for the scientific method. By evaluating a null hypothesis in addition to another hypothesis, researchers can support their conclusions with a higher level of confidence. Below are examples of how you might formulate a null hypothesis to fit certain questions.
Crafting a Null Hypothesis: A Guide to Writing it Right In the realm of scientific research and statistical analysis, crafting a precise null hypothesis is a fundamental step in hypothesis testing. This guide will navigate through the intricacies of forming a null hypothesis that is both clear and testable, setting the stage for robust and reliable research outcomes. We'll explore the ...
Are you working on a research project and struggling with how to write a null hypothesis? Well, you've come to the right place! Keep reading to learn everything you need to know about the null hypothesis, including a review of what it is, how it relates to your research question and your alternative hypothesis, as well as how to use it in different types of studies.
The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test. When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant.
The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain oppos...
A null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the starting point for statistical testing. Formulating a null hypothesis involves defining a clear and concise research question, stating the hypothesis in a way that allows for empirical testing, and considering the potential for Type I errors.
The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in. Hypothesis testing example You want to test whether there is a relationship between gender and height.
Get null hypothesis examples. Learn the difference between the null hypothesis and alternative hypothesis.
We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the p-value (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.
The statistical hypothesis tests for a pattern, and helps you decide, based on the test statistic, if there is no pattern (NULL) or there is a pattern (ALTERNATIVE) at some specific level of probability.
Null Hypothesis Overview The null hypothesis, H 0 is the commonly accepted fact; it is the opposite of the alternate hypothesis. Researchers work to reject, nullify or disprove the null hypothesis. Researchers come up with an alternate hypothesis, one that they think explains a phenomenon, and then work to reject the null hypothesis. Read on or watch the video for more information.
Learn how to formulate and test null and alternative hypotheses in statistics with examples and exercises from this LibreTexts course.
Null Hypothesis Examples. "Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a ...
10.1 - Setting the Hypotheses: Examples A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations ...
The research question, when stated as one sentence, is your Research Hypothesis. In some disciplines, the hypothesis is called a "thesis statement."Other words for "hypothesized" are "posited," "theorized" or "proposed". Remember, your hypothesis must REQUIRE two or more disciplines, one of which is law.
Ha: The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0. Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.
A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses.
Basic definitions. The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise. The statement being tested in a test of statistical significance is called the null ...
When using the p-value to evaluate a hypothesis test, the following rhymes can come in handy:. If the p-value is low, the null must go.. If the p-value is high, the null must fly.. This memory aid relates a p-value less than the established alpha ("the p-value is low") as rejecting the null hypothesis and, likewise, relates a p-value higher than the established alpha ("the p-value is ...
The null hypothesis is a hypothesis in which the sample observation results from chance. Learn the definition, principles, and types of the null hypothesis at BYJU'S.
Master Null Hypothesis with 60+ examples, step-by-step writing guide, and free PDFs 📘. Essential for students, educators, and researchers in any field!
The p value determines statistical significance. An extremely low p value indicates high statistical significance, while a high p value means low or no statistical significance. Example: Hypothesis testing. To test your hypothesis, you first collect data from two groups. The experimental group actively smiles, while the control group does not.