Inferential statistical procedures generally fall into two possible categorizations: parametric and non-parametric. Depending on the level of the data you plan to examine (e.g., nominal, ordinal, continuous), a particular statistical approach should be followed. Parametric tests rely on the assumption that the data you are testing resembles a particular distribution (often a normal or “bell-shaped” distribution). Non-parametric tests are frequently referred to as distribution-free tests because there are not strict assumptions to check in regards to the distribution of the data.
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As a general rule of thumb, when the dependent variable’s level of measurement is nominal (categorical) or ordinal, then a non-parametric test should be selected. When the dependent variable is measured on a continuous scale, then a parametric test should typically be selected. Fortunately, the most frequently used parametric analyses have non-parametric counterparts. This can be useful when the assumptions of a parametric test are violated because you can choose the non-parametric alternative as a backup analysis.
The most prevalent parametric tests to examine for differences between discrete groups are the independent samples t-test and the analysis of variance (ANOVA). An independent samples t-test assesses for differences in a continuous dependent variable between two groups. An ANOVA assesses for difference in a continuous dependent variable between two or more groups. The non-parametric alternative to these tests are the Mann-Whitney U test and the Kruskal-Wallis test, respectively. These alternatives are appropriate to use when the dependent variable is measured on an ordinal scale, or if the parametric assumptions are not met.
The most frequent parametric test to examine for strength of association between two variables is a Pearson correlation (r). A Pearson correlation is used when assessing the relationship between two continuous variables. The non-parametric equivalent to the Pearson correlation is the Spearman correlation (ρ), and is appropriate when at least one of the variables is measured on an ordinal scale.
When examining for differences in a continuous dependent variable among one group over a period of time (ex: pretest and posttest), the dependent samples t-test and repeated measures ANOVA are the most applicable parametric procedures. A dependent samples t-test compares scores at two different points in time. A repeated measures ANOVA incorporates two or more points in time for comparison. The non-parametric versions of these two tests are the Wilcoxon-Signed Rank test and the Friedman ANOVA, respectively.