Summary of Statistical Tests

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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