15.4 REVIEW OF CONCEPTS
Nonparametric hypothesis tests are used when a study’s design does not meet the assumptions of a parametric test. This often occurs when there is a nominal or ordinal dependent variable, or a small sample in which the data suggest a skewed population distribution. Given the choice, we should use a parametric test because these tests tend to have more statistical power and because we can more frequently calculate confidence intervals and effect sizes for parametric hypothesis tests.
We use the chi-square test for goodness of fit when we have only one variable and it is nominal. We use the chi-square test for independence when we have two nominal variables; typically, for the purposes of articulating hypotheses, one variable is thought of as the independent variable and the other is thought of as the dependent variable. With both chi-square tests, we analyze whether the data that we observe match what we would expect according to the null hypothesis. Both tests use the same basic six steps of hypothesis testing that we learned previously. We usually calculate an effect size as well; the most commonly calculated effect size with chi square is Cramér’s V, also called Cramér’s phi. We can also create a graph that depicts the conditional proportions of an outcome for each group. Alternately, we can calculate relative risk (relative likelihood or relative chance) to more easily compare the rates of certain outcomes in each of two groups.
Ordinal Data and Correlation
The nonparametric parallel to the Pearson correlation coefficient is the Spearman rank-order correlation coefficient, a statistic that is interpreted just like its parametric cousin with respect to magnitude and direction. The Mann–Whitney U test is the nonparametric parallel of the independent-samples t test. The same six steps of hypothesis testing are used for both parametric and nonparametric tests, but the steps and the calculations for the nonparametric tests tend to be simpler.