What statistical tests should be used to assess the significance of differences between groups and how do they differ?

To assess the significance of differences between groups, statistical tests are chosen depending on the type of data and distribution:

• Student's t-test — for comparing the means of two groups with a normal distribution and equal variances.
• Mann-Whitney U test — a non-parametric test for comparing two independent groups when data are not normally distributed.
• ANOVA (Analysis of Variance) — for comparing the means of more than two groups with normality and homogeneity of variances.
• Kruskal-Wallis test — a non-parametric analogue of ANOVA for multiple groups.
• χ²-test (Chi-square test) — for categorical data to test the association between groups.

Differences:

• Parametric tests (t-test, ANOVA) assume normal distribution and equal variances.
• Non-parametric tests (Mann-Whitney, Kruskal-Wallis) do not require these assumptions and are applicable to ordinal or non-normal data.

The choice of test depends on the data and the hypothesis you are testing.