Section author: Danielle J. Navarro and David R. Foxcroft


  • A one sample *t*-test is used to compare a single sample mean against a hypothesised value for the population mean.
  • An independent samples *t*-test is used to compare the means of two groups, and tests the null hypothesis that they have the same mean. It comes in two forms: the Student test assumes that the groups have the same standard deviation, the Welch test does not.
  • A paired samples *t*-test is used when you have two scores from each person, and you want to test the null hypothesis that the two scores have the same mean. It is equivalent to taking the difference between the two scores for each person, and then running a one sample t-test on the difference scores.
  • One-sided tests are perfectly legitimate as long as they are pre-planned.
  • Effect size calculations for the difference between means can be calculated via the Cohen’s d-statistic.
  • You can check the normality of a sample using QQ plots and the Shapiro-Wilk test.
  • If your data are non-normal, you can use Mann-Whitney or Wilcoxon tests instead of t-tests.