Paired t-Test
Computes the paired t-test, used when you measure the same subjects twice — before and after a treatment, or by two methods. It works with the differences of each pair and tests whether the mean difference is compatible with zero. By removing the variability between subjects, it's usually far more powerful than comparing two independent groups. The tool returns the t statistic, the degrees of freedom and the two-sided p-value. Enter the two paired series.
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Paired t-Test
Computes the paired t-test, used when you measure the same subjects twice — before and after a treatment, or by two methods. It works with the differences of each pair and tests whether the mean difference is compatible with zero. By removing the variability between subjects, it's usually far more powerful than comparing two independent groups. The tool returns the t statistic, the degrees of freedom and the two-sided p-value. Enter the two paired series.
Measuring the same thing twice to gain power
When you compare two groups made up of different people, part of the variation you see comes from the differences between individuals themselves, and that makes it harder to spot the treatment effect. The paired design gets around this noise by measuring each individual twice, so each one serves as its own control. The paired t-test is the tool for analyzing that design.
Instead of working with the two sets of values, the test reduces everything to the differences within each pair. The question becomes simple: is that mean difference compatible with zero? The statistic divides the mean of the differences by its standard error, and since the variation between individuals was removed in the subtraction, what's left is a test typically more sensitive than the one for independent groups.
Enter the two paired series, in the same order of subjects. The tool returns the t statistic, the degrees of freedom and the two-sided p-value. If the data don't look normal, consider the non-parametric version, the Wilcoxon signed-rank test, which follows the same pairing logic but drops the normality assumption.
Related Tools
McNemar's Test (Paired)
Computes McNemar's test, used to compare two paired proportions — when the same subjects are measured twice (before and after, or by two methods). Unlike the two-proportion test, which treats the groups as independent, McNemar looks only at the cases that switched classification (the discordant cells b and c of the 2×2 table), ignoring those that stayed the same. The continuity-corrected version follows a chi-square with 1 degree of freedom. Enter the two discordant counts.
Wilcoxon Signed-Rank Test
Computes the Wilcoxon signed-rank test, the non-parametric alternative to the paired t-test. When you measure the same subjects twice — before and after a treatment — and the data don't follow a normal distribution, this is the test to use. It works with the differences between pairs: it ranks the magnitudes of those differences, assigns ranks and separately sums the ranks of the positive and negative differences. The tool computes W+, W− and the normal approximation z, with a tie correction. Enter the two paired series.
Z-Test for a Mean (Known σ)
Computes the z-test for a mean when the population standard deviation is known. It's the simplest case of hypothesis testing about a mean: the statistic measures how many standard errors separate the observed mean from the hypothesized value. When σ is known (or the sample is large), the normal distribution is used instead of the t. The tool returns the z statistic and the two-sided p-value. Enter the sample mean, the hypothesized mean, the population standard deviation and the sample size.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.