17.1.4—T-test to compare means of two samples

A t-test compares the means of two samples to judge whether their difference is larger than would be expected from variation within the samples. It tests the difference between means, not whether the data are biologically important by themselves.

• Use the test for two sets of continuous data that are approximately normally distributed, with approximately equal standard deviations; calculate a standard deviation for each sample.
• State the null hypothesis: there is no statistically significant difference between the two population means, and any observed difference is due to chance.
• Design the comparison fairly: keep relevant conditions the same, use comparable samples and sample sizes where appropriate, and identify the measured variable before analysing the means.

• Calculate or obtain each sample mean and standard deviation, then use the supplied t-test formula.
• Calculate degrees of freedom: v = (n₁ − 1) + (n₂ − 1).
• Compare the calculated t with the critical value for v at the chosen significance level. If t is greater than the critical value, reject the null hypothesis; otherwise, do not reject it.
• State the conclusion about whether the difference between the two means is statistically significant and relate it to the experimental comparison.

Rejecting the null hypothesis supports a statistically significant difference; it does not prove causation or establish biological importance. Failing to reject it does not prove that the means are identical. Do not say that “the data” are significant: the difference between the means is significant or not.