Differentiate parametric tests from nonparametric tests.
Parametric tests have interval or ratio outcome variables that must be normally distributed. Nonparametric tests can be done on nominal or ordinal outcome variables and don’t require a normal distribution. Less restricted by assumptions, nonparametric tests often have less power than parametric tests.
Calculate and interpret a chi-square goodness-of-fit test.
The chi-square goodness-of-fit test is a nonparametric, single-sample test for use with a nominal outcome variable. It compares the observed frequencies to the expected frequencies to calculate a chi-square value. Interpretation concerns whether the null hypothesis was rejected and, if so, what the direction of the difference was.
Calculate and interpret a chi-square test of independence.
A chi-square test of independence determines whether two or more populations differ on a nominal-level outcome variable. Data for it are arrayed in a contingency table, which shows the degree to which the outcome variable is determined by the explanatory variable. The chi-square value is calculated from the discrepancy between the observed frequencies and the expected frequencies. In the interpretation, three questions are addressed: (1) whether the null hypothesis was rejected, (2) what the direction of the difference is, and (3) how big the effect is.
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Know when to use a Spearman rank-order correlation coefficient and a Mann–Whitney U test.
The Spearman rank-order correlation coefficient, used with ordinal-level data, is the nonparametric alternative to Pearson r, the correlation coefficient used with interval/ratio-level data. The Mann–Whitney U test, used with an ordinal outcome variable, is the nonparametric alternative to an independent-samples t test.