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t-test calculator

Compare two groups and get the effect size and interval, not just a p-value.

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Test

Welch's t-test — does not assume equal variances. The sensible default.

Paste at least two values into each group.

Formuladifference ± t(1−α/2, df) × SE
ModelWelch's t-test

If your values are technical replicates from a smaller number of independent experiments, your n is the number of experiments. Pooling them here will overstate significance.

When to use this

Use this to compare two groups. Welch’s test is the sensible default and the tool reports the difference with its confidence interval and an effect size, because a p-value on its own does not tell you whether the difference matters.

Worked example

Treated versus control, six replicates each.

Test
Welch’s unpaired
Group sizes
6 and 6

Result

Difference of means with a 95% interval

Read the interval first: if it spans values that would and would not change your conclusion, the experiment is underpowered whatever the p-value says.

What people get wrong

  • Pooling technical replicates as though they were independent. Three dishes from one experiment is an n of one, and this is the commonest way papers report significance that is not there.
  • Choosing the paired test because the groups are the same size. Pairing requires each measurement to have a genuine partner — the same animal, the same dish, before and after.
  • Reporting only the p-value. Give the difference and its interval; the p-value belongs last and small.

Questions

+Welch’s or Student’s?

Welch’s, as the default. It costs almost nothing when the variances match and protects you when they do not, so there is little reason to assume equal variance.

+What if my data are not normal?

Mann–Whitney is the usual fallback, though at small n it has little power. Note that it returns no confidence interval here, because it does not estimate one.

+What effect size does it report?

Hedges’ g, which applies a small-sample correction to Cohen’s d. The correction vanishes at large n, so there is no case for the uncorrected version.

Related tools

Science last reviewed .