19: Repeated Measures
19.1 Measuring Changes Over Time
In research, particularly when examining changes over time or the impact of different conditions on the same subjects, repeated measures tests are essential. These tests account for the fact that the same participants are measured multiple times, allowing researchers to examine within-subject variations rather than between-subject differences. The advantage of repeated measures is that they reduce the variability that can arise from individual differences, offering greater statistical power and more sensitive analyses.
This chapter will cover several statistical tests commonly used with repeated measures data. These include the Paired Samples T-Test, Wilcoxon Rank Test, McNemar Test, Repeated Measures ANOVA, Friedman’s Test, and Cochran’s Q Test. For each test, we will discuss the key assumptions, when the test is appropriate, and how to apply it in research.
19.2 Paired Samples T-Test
The Paired Samples T-Test (also known as the dependent samples t-test) is used to compare the means of two related groups, such as measurements taken before and after an intervention on the same subjects. The test examines whether the mean difference between the paired observations is significantly different from zero.
The assumptions for the Paired Samples T-Test include independence of the differences between pairs, normality of the differences (especially critical for small sample sizes), and that the dependent variable is continuous. If the assumption of normality is violated, the Wilcoxon Signed-Rank Test (a non-parametric alternative) should be used.
In Jamovi, the Paired Samples T-Test can be run by selecting Analyses > T-Tests > Paired Samples T-Test, choosing the variables for comparison, and generating the test results, which will provide the t-statistic, degrees of freedom, and p-value.
How To: Paired Samples T-Test
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19.3 Wilcoxon Rank Test
The Wilcoxon Rank Test is a non-parametric alternative to the Paired Samples T-Test. It is used when the assumption of normality for the paired differences is violated, and it is ideal for ordinal data or non-normally distributed continuous data.
The assumptions for the Wilcoxon Rank Test include the data points coming from two related groups, typically measured at two different times or conditions, and the data should be at least ordinal. The test still works with continuous data but does not assume a normal distribution. This test is appropriate when you need a more robust method for comparing two related groups without relying on normality.
In Jamovi, this test can be run by going to Analyses > Non-Parametric Tests > Wilcoxon Signed Rank, selecting the variables to compare, and then generating the test statistic and p-value.
How To: Wilcoxon Rank Test
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19.4 McNemar Test
The McNemar Test is used for binary data (e.g., yes/no, success/failure) in a 2×2 contingency table. It is typically applied when comparing paired nominal data, such as responses to a treatment before and after an intervention. The test assesses whether the proportions of changes in responses (e.g., success to failure and failure to success) are statistically significant.
The assumptions for the McNemar Test include binary data and related samples, meaning the same subjects are measured at two different times or under two different conditions. If the data is not binary, consider using tests like Cochran’s Q for more than two categories.
In Jamovi, the McNemar Test can be performed by selecting Analyses > Frequencies > McNemar Test, choosing the binary variable at two different time points, and generating the test results.
How To: McNemar Test
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19.5 Repeated Measures ANOVA
The Repeated Measures ANOVA is used when multiple measurements are taken from the same subjects over time or under different conditions. This test assesses the effects of independent variables on the dependent variable, while also allowing for the analysis of interaction effects between factors.
The assumptions for Repeated Measures ANOVA include independence of observations (across subjects), normality of the dependent variable for each level of the independent variable, and sphericity, which refers to the equality of variances of the differences between all possible pairs of conditions. If the assumption of sphericity is violated, a Greenhouse-Geisser correction or Huynh-Feldt correction can be applied.
In Jamovi, the Repeated Measures ANOVA can be accessed through Analyses > ANOVA > Repeated Measures ANOVA, where you can select the dependent variable(s), specify the factors and levels, and run the analysis. The results will include F-statistics, p-values, and post-hoc tests for significant effects.
How To: Repeated Measures ANOVA
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19.6 Friedman’s Test
The Friedman Test is a non-parametric alternative to the Repeated Measures ANOVA, used when the assumptions of normality for the repeated measures data are violated. This test is suitable when the data is ordinal or continuous, and it compares the ranks across different conditions or time points for the same subjects.
The assumptions for the Friedman Test include related samples (i.e., the same subjects are measured multiple times), ordinal or continuous data, and independent observations. It does not require the data to be normally distributed, making it an ideal choice when the Repeated Measures ANOVA assumptions are not met.
In Jamovi, the Friedman Test can be conducted by selecting Analyses > Non-Parametric Tests > Friedman Test, choosing the repeated measures variables, and generating the test statistic and p-value.
How To: Friedman’s Test
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19.7 Cochran’s Q Test
The Cochran’s Q Test is a non-parametric test used for binary outcomes measured at more than two related conditions or time points. It is an extension of the McNemar test and is used when binary data is collected across three or more related groups. This test is ideal for situations where you have multiple time points or conditions and want to examine whether the proportions of success/failure change across them.
The assumptions for Cochran’s Q Test include binary data, related samples (the same subjects measured at multiple points), and independent observations across subjects. If the data is not binary, alternative tests like the Chi-Square test of independence should be considered.
In Jamovi, Cochran’s Q Test can be run by selecting Analyses > Non-Parametric Tests > Cochran Q Test, choosing the binary variables measured across multiple time points or conditions, and generating the test results.
How To: Cochran’s Q
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19.8 Choosing the Right Test
Choosing the correct test for repeated measures depends on the type of data, the number of groups or conditions, and the assumptions of the tests:
- Use the paired samples t-test for comparing the means of two related groups with continuous data.
- Use the Wilcoxon rank test for ordinal or non-normally distributed data with two related groups.
- Use the McNemar test for binary data with two related groups.
- Use Repeated Measures ANOVA for analyzing the effects of multiple measurements on the same subjects, including interaction effects or covariates.
- Use Friedman’s test when the assumptions of Repeated Measures ANOVA are violated, particularly for ordinal or non-normally distributed data.
- Use Cochran’s Q test for binary outcomes measured at multiple time points or conditions.
Chapter 19 Summary and Key Takeaways
In this chapter, we explored several tests for repeated measures data, including the Paired Samples T-Test for comparing two related groups, the Wilcoxon Rank Test as a non-parametric alternative when normality is violated, and the McNemar Test for binary data in a 2×2 contingency table. We also discussed the Repeated Measures ANOVA, which allows for testing the effects of multiple measurements on the same subjects, including interaction effects and covariates, as well as its non-parametric counterpart, the Friedman’s Test. The Cochran’s Q Test was a non-parametric test for binary data across more than two related groups. By understanding the assumptions and applications of these tests and how to handle violations, researchers can confidently analyze repeated measures data in applied research.
- Paired samples t-test and Wilcoxon Rank Test are used for comparing two related groups.
- Repeated Measures ANOVA allows testing for interactions and covariates with multiple time points or conditions.
- Friedman’s Test is the non-parametric alternative to Repeated Measures ANOVA for non-normal data.
- Cochran’s Q Test is used for binary data across more than two related conditions or time points.