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.
|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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