Paired Samples t-test
Also known as: dependent samples t-test, repeated measures t-test, matched-pairs t-test, eşleştirilmiş örneklem t-testi
The paired samples t-test is a parametric hypothesis test that compares two measurements taken on the same subjects — such as a before and after reading — to decide whether the average change differs from zero. It rests on the t-distribution introduced by Student (W. S. Gosset) in 1908 and works on the within-subject difference scores rather than the raw measurements.
Key highlights
- By removing stable between-subject differences it is more powerful than an independent t-test for the same effect.
- Reports an interpretable paired effect size (Cohen's d) alongside the p-value and confidence interval.
- Simple, widely accepted, and available in every analysis package.
Intuition
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How it works
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When to use it
Use it when the same units are measured twice on a single continuous outcome — a pre-test/post-test design or any matched-pairs setup. Two assumptions should hold: the difference scores are approximately normally distributed (check with Shapiro-Wilk on the differences), and the pairs are genuinely linked. A sample of at least about 20 pairs is recommended so the normality of the differences can be assessed and the test has adequate power. If the differences are clearly non-normal or the sample is very small, use the nonparametric Wilcoxon signed-rank test instead.
Strengths & limitations
- By removing stable between-subject differences it is more powerful than an independent t-test for the same effect.
- Reports an interpretable paired effect size (Cohen's d) alongside the p-value and confidence interval.
- Simple, widely accepted, and available in every analysis package.
- Requires genuinely paired or matched data; it cannot compare two independent groups.
- Relies on the normality of the difference scores, which is fragile in small samples.
- Limited to exactly two repeated measurements; three or more time points call for repeated-measures ANOVA.
Common pitfalls
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Applications
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Frequently asked
How is this different from the independent t-test?
The independent t-test compares two separate groups, while the paired t-test compares two measurements on the same subjects. Because the pairing removes stable individual differences, the paired test is usually more sensitive when the data are genuinely linked.
What if the difference scores are not normal?
Normality applies to the differences, not the raw values. If a Shapiro-Wilk test on the differences is significant or the sample is very small, switch to the Wilcoxon signed-rank test, the nonparametric counterpart.
How many pairs do I need?
At least about 20 pairs is recommended so the normality of the difference scores can be assessed and the test retains adequate power. With fewer pairs the normality assumption is hard to check and power drops sharply.
Why report an effect size?
The p-value only tells you whether the average change is detectable, not how large it is. Cohen's d for paired data expresses the mean difference in standard-deviation units, so you can judge practical importance alongside the mean difference and its 95% confidence interval.
Sources
- 1.Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE.ISBN 978-1446249185
- 2.Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.
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Cite this page
ScholarGate. (2026, June 1). Paired t-test. ScholarGate. https://scholargate.app/statistics/paired-t-test