Name: mcnemar's test for paired proportions
Uploaded: 2025-01-09T15:14:09.000Z
Duration: 1 min 23 s
Channel: JoVE

McNemar&#39;s test applies to paired nominal data presented in two-by-two contingency tables. This is a special case of randomized block design, where individuals are evaluated only twice.
For example, an ant species is evaluated in an experimental setting for its response to the artificial odor of its potential prey.
30 individuals are subjected to test arenas measuring 5 and 10 cm, one half of which is infused with the odor, and the other is a control.
The ants that move toward the odor are scored +, and the ones that move towards the control are scored -. Next, the two-by-two contingency table for 5 and 10 cm arenas is as follows.
Here, the null hypothesis is that the proportions in these two trials are the same, mathematically expressed as follows. If the change in the proportion between two trials is significant, the null hypothesis is rejected.
McNemar&#39;s test statistic is computed by the following expression.
As these values approximate chi-square distribution, the degree of freedom is one, and there is no evidence of any significant change in the behavioral response.

mcnemar's test

McNemar's Test

McNemar&#39;s Test is a nonparametric statistical test used to determine if there is a significant difference in proportions between two related groups when the outcome is binary (e.g., yes/no, success/failure). It is beneficial when we have paired data, such as pre-test/post-test designs, where the same subjects are measured under two different conditions. The test is named after the statistician Quinn McNemar, who introduced it in 1947. It is commonly used in situations where subjects are measured before and after a treatment or in matched-pair study designs.
Assumptions of McNemar&#39;s Test
For McNemar&#39;s test to produce valid results, the following assumptions must be met:
<ol>
	<li>Paired Samples: The data must come from matched pairs, where each subject in one group corresponds to a subject in the other group (e.g., pre-post data or matched-pair design).</li>
	<li>Dichotomous Outcome: The test is designed for binary outcomes, such as yes/no, success/failure, or presence/absence.</li>
	<li>Independence of Pairs: Each pair should be independent of other pairs in the study. This means that the pairs (not individual observations) should be unrelated to each other.</li>
	<li>Sufficient Sample Size: McNemar&#39;s test is robust for small sample sizes, but reliability decreases with very small samples. Generally, a minimum of 10 discordant pairs&#8212;where the outcomes differ between conditions&#8212;is recommended for meaningful results. With a small number of discordant pairs, the test may lack the power needed to detect a true difference between the paired conditions.</li>
</ol>
Applicability and Conditions
McNemar&#39;s test is particularly suited for the following situations:
<ol>
	<li>Pre-Post Study Designs: Used to assess the effect of an intervention by comparing the responses of the same subjects before and after treatment.</li>
	<li>Matched-Pair Studies: Applied when subjects are matched based on certain characteristics and then exposed to different treatments or conditions.</li>
	<li>Clinical Trials: Here, the test is used to compare the effectiveness of treatments by analyzing the same group of patients at two different points in time.</li>
</ol>
McNemar&#39;s test is a valuable tool for analyzing paired nominal data, particularly in medical and psychological research, where pre-post designs and matched-pair studies are commonly used. By understanding and meeting the assumptions of the test, researchers can apply McNemar&#39;s test to draw reliable conclusions about differences in proportions between two related groups.

McNemar&#39;s test applies to paired nominal data presented in two-by-two contingency tables. This is a special case of randomized block design, where ...

Education

JoVE Core

Statistics

Unit 1

Nonparametric Statistics

KEY TERMS AND CONCEPTS

mcnemar's test for paired proportions

McNemar's Test compares paired proportions when the outcome has only two choices, such as yes/no, success/failure, or presence/absence. It is a nonparametric statistical test, so it is useful when the data come from related groups rather than independent groups. The test is often used with pre-test and post-test data, where the same subjects are measured under two conditions.

The test is named after the statistician Quinn McNemar, who introduced it in 1947. It is commonly used in matched-pair study designs and in situations where the same people are measured before and after a treatment. In these settings, researchers want to know whether the proportion of answers changes in a meaningful way.

McNemar's Test works best when the samples are paired. Each subject in one group must match a subject in the other group. The outcome must also be dichotomous, which means it has two possible categories. In addition, each pair should be independent of the other pairs in the study.

Sample size also matters. McNemar's Test can handle small samples, but results become less reliable when the sample is very small. A minimum of 10 discordant pairs is generally recommended. Discordant pairs are the pairs in which the two conditions give different outcomes. If there are too few of these pairs, the test may not have enough power to detect a real difference.

McNemar's Test is especially useful in pre-post study designs, matched-pair studies, and clinical trials. In clinical research, it can compare treatment effects by looking at the same group of patients at two different points in time. It is a valuable tool for analyzing paired nominal data, especially in medical and psychological research where these study designs are common.

McNemar's Test for Paired Proportions

introduction to nonparametric statistics

Nonparametric Tests for Unusual Data

Nonparametric statistics are useful when data do not fit the usual assumptions for parametric tests. Parametric tests depend on a known population distribution and specific values such as the mean and standard deviation. Nonparametric tests do not require those conditions, so they are often used with small samples, skewed data, or ordinal and categorical variables. These methods are flexible because they work with data that do not meet requirements like normal distribution or equal variance.

ranks

Rank Ordering in Nonparametric Statistics

Rank ordering is a nonparametric statistics method that arranges data by a chosen criterion. It is useful for nominal and ordinal data, where values are grouped or ordered rather than measured on a scale. Because it needs fewer assumptions about the population, it is often easier to apply and interpret than parametric methods. To rank data, items are sorted first and then assigned a position. A set of weather days can be ordered from hottest to coldest, and cities can be arranged from smallest...

introduction to the sign test

Using the Sign Test for Paired Data

The sign test is a nonparametric statistics method for paired data, nominal data, and claims about a population median. It uses only the direction of change, so it does not rely on assumptions about the data distribution. That makes it useful when data do not fit the normal distribution requirements of many parametric tests. Researchers can use the sign test to compare two related measurements, such as pre- and post-treatment results in a medical study. In that example, a positive sign can...

sign test for matched pairs

Matched Pair Changes: The Sign Test

The sign test for matched pairs compares two related samples. It is often used to check the effect of an intervention on one of the pairs. This method is useful when the data distribution is unknown. It is also helpful for small sample sizes. The test usually looks at pre- and post-treatment measurements from the same subjects. It asks whether the median values of the two related samples are different. To do this, the differences between each pair of observations are calculated first. The test...

sign test for nominal data

Testing Preferences with the Sign Test

The sign test is a nonparametric method for testing a single sample median or comparing the medians of two related samples. It is useful when the data are nominal, which means the values are categories such as names, labels, or preferences. Because nominal data do not have a natural order, analysis focuses on population proportions instead of mean or median values from continuous data. A simple example is a survey about pet preference. If some people choose dogs and others choose cats, the...

sign test for median of single population

sign-test-for-median-of-single-population

Single-Population Sign Test for a Median

The single-population sign test checks whether one sample median matches a chosen value. It is a nonparametric method, so it is useful when the data do not follow a known distribution. It is also helpful for small samples or when the usual assumptions for parametric tests are not met. The test starts with a null hypothesis that the population median equals a specific number. The alternative hypothesis can state that the median is different from, less than, or greater than that number. The...

wilcoxon signed-ranks test for matched pairs

wilcoxon-signed-ranks-test-for-matched-pairs

Testing Paired Data with Wilcoxon Signs

The Wilcoxon signed-rank test checks paired data by using both the size and the direction of the differences. It is a nonparametric test, which means it does not require the data to follow a normal distribution. It tests whether the median of the differences in a population of matched pairs is zero. This test works best when the data come in matched pairs, such as two measurements from the same subject or linked observations. The differences between each pair should also have an approximately...

wilcoxon signed-ranks test for median of single population

wilcoxon-signed-ranks-test-for-median-of-single-population

Wilcoxon Signed-Rank Test Using Ranked Differences

The Wilcoxon signed-rank test uses ranked differences to check whether a single population median matches a chosen value. It is a nonparametric test, so it does not require the data to follow a normal distribution. That makes it useful for small samples and for data that are not normal. The test starts by finding the difference, d, between each observation and the hypothesized median. The absolute values of those differences are then ranked from smallest to largest, and ties get the average...

wilcoxon rank-sum test

Comparing Two Groups with Rank Sums

The Wilcoxon rank-sum test compares two independent groups by using ranks instead of raw numbers. It is also called the Mann-Whitney U test. This nonparametric test helps show whether the two groups come from different distributions. The test is meant for two independent populations. The samples should be randomly drawn. The data must be ordinal, or it must be possible to put the data in order and rank it. The null hypothesis says the medians of the two populations are the same. The...

bootstrapping

Bootstrapping in Small Sample Statistics

Bootstrapping is a statistical resampling method used to estimate population parameters from an existing sample. It builds on the idea of the word bootstrap, which first appeared in the 19th century as a metaphor for doing something independently. In statistics, the method was developed by Dr. Bradley Efron in 1979. Bootstrapping is also called bootstrap resampling. It works by drawing many random samples, with replacement, from the original dataset. Each bootstrap sample has the same size as...

the anderson-darling test

Anderson-Darling Test for Goodness of Fit

The Anderson-Darling test checks whether a data sample fits a specific theoretical distribution. It compares the sample’s empirical cumulative distribution function, or ECDF, with the cumulative distribution function, or CDF, of the distribution being tested. This makes it a useful goodness-of-fit method when the population distribution is uncertain. Unlike parametric tests, the Anderson-Darling test does not require assumptions about specific distribution parameters. Its critical values...

spearman's rank correlation test

Using Ranks to Measure Correlation

Spearman's rank correlation test measures the link between two variables by using ranks instead of raw values. It is a nonparametric method, so it is useful when the data distribution is unknown or when the normality assumption does not hold. The test is also known as Spearman's rho and is named after Dr. Charles Edward Spearman, an English psychologist and statistician. This method acts as the nonparametric counterpart to Pearson's correlation coefficient. Pearson's correlation measures only...

kendall's tau test

Kendall Tau for Rank Correlation

Kendall's tau is a rank correlation test for checking whether two variables are related. It is also called the Kendall rank coefficient test. Because it is nonparametric, it can be used when the sample and population distributions are unknown. The test was developed in 1938 by British statistician Sir Maurice George Kendall. Its tau coefficient, written as τ, ranges from -1 to +1. A value of +1 means the two rankings are perfectly similar and show a strong positive correlation. A value of -1...

kruskal-wallis test

Kruskal-Wallis Test for Group Comparison

The Kruskal-Wallis test compares three or more independent groups when the data is not suited to a one-way ANOVA. It is a nonparametric test, which means it does not rely on the normal distribution needed for parametric methods. It is often used with one ordinal dependent variable, so it works well for ranked or ordered data. This test is useful when group data does not meet the assumption of equal variances or when the data shape is not normal. Instead of comparing means, the Kruskal-Wallis...

wald-wolfowitz runs test i

Runs Test for Randomness in Sequences

The Wald-Wolfowitz runs test checks whether the order of values in a sequence is random. It is also called the runs test. This nonparametric statistical test is used for ordered data, even when the population and sample distributions are not known. The method focuses on runs. A run is a continuous stretch of the same symbol, such as a series of positive values or a series of negative values. It can also be used with binary data, such as successes and failures, or with other two-category...

wald-wolfowitz runs test ii

Runs Test for Randomness in Ordered Data

The Wald-Wolfowitz runs test checks whether ordered data is random or shows a pattern. A run is a consecutive sequence of similar items. If the number of runs is much higher or lower than expected, the data is considered non-random and may contain a detectable structure. The test works with binary data such as + and −, or 1s and 0s. For data with two categories, the categories are first converted into binary choices. DNA sequences can be tested directly because categories like A, T, G, and C...

behrens&#8211;fisher test

Unequal-Variance Mean Comparison Test

The Behrens-Fisher test compares the means of two normally distributed populations when their variances are not equal. It is used when the usual Student’s t-test is not a good fit because that test assumes equal variances. This makes the Behrens-Fisher test useful for two independent samples that follow normality but do not share variance homogeneity. The method is especially helpful with small sample sizes. In that setting, unequal variances can affect how reliable the results are. The test...

fisher&#39;s exact test

Fisher's Exact Test for Small Tables

Fisher's exact test is a statistical significance test for 2x2 contingency tables. It is often used when sample sizes are small and the data are categorical. The test helps scientists check whether two variables may be related. Unlike the chi-squared test, Fisher's exact test does not estimate the P-value. It calculates the exact probability of seeing the observed data, or more extreme results, if the null hypothesis is true. That makes it useful when the chi-squared test assumptions are not...

friedman two-way analysis of variance by ranks

friedman-two-way-analysis-of-variance-by-ranks

Friedman Rank Test for Repeated Measures

Friedman’s Rank Test for Repeated Measures compares related data across several conditions when the usual ANOVA rules do not fit. It is a nonparametric test, so it works well with ordinal data or data that are not normally distributed. It is also useful for matched subjects over time or for repeated measures from the same group. The null hypothesis, H0, says that there is no difference in the distributions of the variables being compared. If H0 is rejected, the results show significant...

cochran's q test

Cochran's Q Test for Repeated Binary Data

Cochran's Q Test compares three or more related groups when the result is binary, meaning a yes/no or 0/1 outcome. It is a nonparametric statistical test, so it does not rely on a normal data pattern. Researchers use it to see whether the proportions differ across multiple conditions or time points for the same subjects. The test is an extension of the McNemar Test. McNemar's Test works with only two related samples, while Cochran's Q Test can handle three or more related samples. The test...

McNemar's Test compares paired proportions when the outcome has only two choices, such as yes/no, success/failure, or presence/absence. It is a nonparametric statistical test, so it is useful when the data come from related groups rather than independent groups. The test is often used with pre-test and post-test data, where the same subjects are measured under two conditions. The test is named after the statistician Quinn McNemar, who introduced it in 1947. It is commonly used in matched-pair...

kendall's coefficient of concordance

Ranking Agreement with Kendall's W

Kendall's Coefficient of Concordance, or Kendall's W, measures how much multiple raters agree when they rank the same set of items. It is a non-parametric statistic, so it works well with ordinal data, which are data written as ranks rather than exact measurements. This measure is useful when several judges or evaluators need to show whether their rankings are consistent. It is often used in research areas such as psychology, medicine, and social sciences. In those settings, people may be...

key terms and concepts

Learn how McNemar's Test compares paired yes/no outcomes in pre-post and matched-pair studies, and see when the test assumptions matter.

McNemar's Test for Paired Proportions | JoVE K12

statistics

JoVE Core Statistics introduces the concepts and application of the collection, analysis, presentation, and interpretation of data to students. These animated lessons provide an understanding of statistics beneficial to students from a wide range of disciplines. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide

McNemar's Test for Paired Proportions

Description

Transcript

Tags