Two-Sample t-Test

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Example: two classes took the same exam. Class A, with 20 students, had a mean of 72 and a standard deviation of 10; class B, with 22 students, a mean of 65 and a standard deviation of 12. Is the difference real, or could it be chance? Change the values to work out your own case.

Mean of group 1 x̄₁ Standard deviation s₁ Size n₁ Mean of group 2 x̄₂ Standard deviation s₂ Size n₂

Step by step

What each term means

t Statistic: How many standard errors separate the two means. Compared with the t distribution, it gives the p-value: the chance of a difference like this by chance alone, if the true means were equal.
Difference of the Means (x̄₁ − x̄₂): What was observed: how far one group's mean landed above the other's, in the units of the data.
Standard Error of the Difference: How much the difference of the means varies from sample to sample. It adds the variances of the two means without assuming the groups have the same variance — which is what defines Welch's test.

When to use it, assumptions and alternatives: the independent-samples t-test in the statistical tests catalog.