Interactive t-test: means, variability and p-values

The relationship to understand

Pooled-variance t-test: t=Δ/[sₚ√(1/n₁+1/n₂)]; sₚ²=[(n₁−1)s₁²+(n₂−1)s₂²]/(n₁+n₂−2), ν=n₁+n₂−2 degrees of freedom.

Try it and interpret

Keep the difference and variability fixed, then increase the sample size: the p-value changes while the difference between means stays the same. With a zero difference, t=0 and p=1.

Assumptions and limitations

This interface illustrates a two-sided pooled-variance test for two independent groups of equal size, at the 5% level. Check normality and equal variances; Welch and paired measurements require a different framework. Displayed points are constructed from the summaries, not real observations.

Go further with the course

This page focuses on one concept. The full chapter (French) contains the reasoning, further examples, slides and FAQ. Demonstration values are computed or constructed within the stated model; they are not new research findings.