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Student’s t-test

The t-test compares two means to see whether the difference is real or could be chance. Use independent samples for two different groups (for example, women and men) and paired samples when the same people are measured twice (before and after a workshop). First, check with the normality test that the scores are normal.

Group A

One per line, or separated by commas or spaces. You can paste a column from Excel.

Group B

One per line, or separated by commas or spaces. You can paste a column from Excel.

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How it’s calculated

Independent samples: t = (M₁ − M₂) / SE. With equal variances (Student’s t), the standard error uses the pooled variance of both groups and there are n₁ + n₂ − 2 degrees of freedom.

Levene’s test (mean-centered, as in SPSS) checks whether the variances are equal. If its p is below 0.05, Welch’s t is reported: it doesn’t assume equal variances and adjusts the degrees of freedom.

Paired samples: each person’s difference is calculated (before − after) and t = mean difference / (SD of differences / √n), with n − 1 degrees of freedom.

Cohen’s d measures the size of the difference in standard deviations: the mean difference divided by the pooled SD, or by the SD of the differences for paired samples.

How to read the result

  • p < 0.05: the difference between the means is statistically significant.
  • Cohen’s d: 0.2 small, 0.5 medium and 0.8 large. Always report it next to the p-value: a difference can be significant but small.
  • If the data aren’t normal and the groups are small (under 30), use the Mann-Whitney U test for independent samples.

Frequently asked questions

Does it match SPSS?
Yes. The SPSS "Independent Samples Test" table shows both rows (equal variances assumed and not assumed) with Levene’s test: they are the same values you see here.
When do I use paired samples?
When each score in group A has a partner in group B: the same person before and after, or matched pairs. Paste the data in the same order in both boxes.
What about three groups or more?
The t-test only compares two. For three or more groups, use ANOVA, or Kruskal-Wallis if the data aren’t normal.
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