Matched Sample T Test Guide
Why This Test Matters
A matched sample t test studies two related measurements. The same subject may be measured before and after a change. A pair may also be formed by matching similar units. The test focuses on the difference inside each pair. This removes much outside variation. It helps reveal whether the average change is meaningful.
The calculator supports raw paired data and summary statistics. Raw data is best when every pair is available. Summary mode is useful when a report gives only the sample size, mean difference, and standard deviation. Both methods lead to the same test statistic when the values are consistent.
Understanding The Decision
The null hypothesis says the true mean difference equals a chosen value. Usually that value is zero. A positive or negative t statistic shows the direction of the sample change. The p value shows how unusual the result is under the null hypothesis. If the p value is less than alpha, the result is significant.
The alternative choice changes the p value. A two tailed test checks any difference. A right tailed test checks whether the mean difference is greater than the null value. A left tailed test checks whether it is smaller. Choose the direction before viewing results.
Effect Size And Interval
Significance alone is not enough. Cohen's dz shows the size of the paired change. It divides the mean difference by the standard deviation of differences. A wider confidence interval means more uncertainty. A narrow interval suggests a more precise estimate.
Good Data Practice
Use complete pairs only. Do not mix unmatched observations into the same test. Check for extreme differences, data entry errors, and unit mistakes. The test works best when pair differences are roughly normal. Large samples are more forgiving, but clear data review still matters.
This tool gives the test statistic, degrees of freedom, p value, confidence interval, standard error, and decision. The exports help document the analysis. Use the report with subject knowledge. Statistical significance should support, not replace, practical judgment.
When Results Need Care
Small samples can be sensitive to unusual pairs. Always inspect the difference list first. If differences are strongly skewed, consider a nonparametric signed rank test instead.