Some statistical tests on different types of variables are summarised in the table below.
For many tests, there are parametric and non-parametric equivalents. The latter term describes tests where one does not have to make so many assumptions about the data being normally distributed. They are thought of as less powerful – less likely to reject null hypotheses – but when the t-test is used inappropriately on small sample sizes of non normally distributed data, a non-parametric test is sometimes much more powerful.
Sometimes, one can use parametric tests for non-normally distributed data. This is because the SE plot is often normally distributed for large sample sizes even when the data are not. A t-test can therefore be performed on non-normally distributed data, provided the sample size is large.
Task |
Parametric test |
Non-parametric test |
Categorical variables |
| Compare a sample to a desired value | One sample t-test | Wilcoxon test | Chi-square test Binomial test |
| Compare two independent samples | Unpaired t-test | Mann-Whitney test | Chi-square test (if large samples)Fisher’s exact test |
| Compare 2 paired samples | Paired t-test | Wilcoxon test | McNemar’s test |
| Compare 3+ unmatched groups | One way ANOVA | Kruskal-Wallis test | Chi-square test |
| Compare 3+ matched groups (e.g. same subject three time points) | Repeated measures ANOVA | Friedman test | Cochrane Q test |
| Association between two continuous variables | Pearson correlation coefficient | Spearman correlation | n/a |
| Determine mathematical relationship between two variables (e.g. prediction) | Linear regression Non-linear regression | Non-parametric regression | Simple logistic regression |
| Determine relationship between 3+ variables | Multiple linear or non-linear regression | Non-parametric regression | Multiple logistic regression |
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