How to use the t-test p-value calculator
Paste the measured values of two groups and the calculator works out each mean and standard deviation itself before returning the t statistic and the p-value. Because it takes raw data rather than pre-computed summary statistics, you can copy a spreadsheet column straight in. Values may be separated by line breaks, commas or spaces, blanks are dropped and duplicates are counted as they are.
In automatic mode the variance ratio of the two groups is run through an F test first. If equal variances are plausible the pooled t test is used, otherwise the Welch test takes over. The test that was applied, the reason for it and the degrees of freedom are all shown, so the result can be quoted directly. A confidence interval for the mean difference and Cohen's d come along too, which keeps statistical significance separate from the size of the real difference.
The p-value is a numerical approximation of the t distribution CDF built from an incomplete beta continued fraction. It agrees with printed t tables to four decimal places, and every intermediate step stays unrounded. Groups with fewer than two values, or groups whose values are all identical, make the t denominator zero, so the calculator explains that instead. Paired-sample tests are not supported.
Frequently asked questions
With similar variances the pooled test has more power, and with very different variances Welch is the safer choice. Automatic mode switches to Welch when the variance ratio F test p-value falls below 0.05.
No. A p-value only says how unlikely the difference is under chance, not how large it is. Read the mean difference and Cohen's d for the size.
No. A standard deviation needs at least two values, and if every value is identical the standard deviation is zero, which makes the t denominator zero.