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T-Test Calculator

Calculate one-sample, paired or Welch t-tests from raw numeric samples. The output keeps the t statistic, degrees of freedom, p-value and standardized effect size separate. Tail selection states the alternative hypothesis instead of assuming every test is two-sided.

Independent observations and an appropriate sampling model are required. Paired rows must correspond. This tool cannot determine whether assumptions hold or whether a result is practically meaningful.

How the calculation works

One-sample/paired t=(mean−null)/(s/√n), df=n−1. Welch t=(meanA−meanB)/√(sA²/nA+sB²/nB), with Welch–Satterthwaite df. P-values use the Student t CDF.

Worked example

For sample 5,6,7,8,9 against null mean 0, mean=7, SD=√2.5 and t≈9.89949 with 4 degrees of freedom. Paired mode first subtracts matching B values from A.

Assumptions and limitations

At least two values per sample and positive variation. Paired samples must have equal counts and correspond row-by-row. Welch compares a zero difference; the null-mean field is for one-sample/paired tests.

Tests assume suitable independent observations and sampling conditions. Statistical significance is not practical significance or causality. Multiple-testing correction and experimental design are outside this calculator.

Sources and editorial responsibility

Maintained by Renvoro Pty Ltd. Sources inform the methods and assumptions shown here; outputs have the limitations described on this page.

Method reviewed 2026-10-13. Calculation standards · Report an issue