Selecting Between Parametric and Non-Parametric Analyses

Quantitative Methodology

Inferential statistical procedures generally fall into two possible categorizations: parametric and non-parametric. Depending on the data level (e.g., nominal, ordinal, continuous), you should follow a specific statistical approach. Parametric tests rely on the assumption that the data you are testing resembles a particular distribution (often a normal or “bell-shaped” distribution). We call non-parametric tests distribution-free because they don’t require strict assumptions about the data’s distribution.

As a general rule, select a non-parametric test when the dependent variable’s level of measurement is nominal (categorical) or ordinal. When the dependent variable is continuous, you should typically select a parametric test.  Fortunately, the most frequently used parametric analyses have non-parametric counterparts.  When the dependent variable is continuous, you should typically select a parametric test.

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. You should use these alternatives when the dependent variable is ordinal or when the data fail to meet the parametric assumptions.

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.

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