Category 4: At Least One Ordinal Variable

If we have a design with even one ordinal variable or a design in which it makes sense to convert the data from scale to ordinal, then we have several choices, as seen in Table E-4. All these choices have parallel parametric hypothesis tests, as seen in Table E-5. For situations in which we want to investigate the relation between two ordinal variables, we use the Spearman rank-order correlation coefficient. For situations in which we have a within-groups research design and two groups, we use the Wilcoxon signed-rank test. When we have a between-groups design with two groups, we use a Mann–Whitney U test. And when we have a between-groups design with more than two groups, we use a Kruskal–Wallis H test.

Table : TABLE E.4 Category 4 Statistics When at least one variable is ordinal, we have several choices. If both variables are ordinal, or can be converted to ordinal, and we are interested in quantifying the relation between them, we use the Spearman rank-order correlation coefficient. If the independent variable is nominal and the dependent variable is ordinal, we choose the correct nonparametric test based on the research design and the number of levels of the independent variable.
Type of Independent Variable (And Number of Levels, If Applicable) Research Design Question to Be Answered Hypothesis Test
Ordinal Not applicable Are two variables related? Spearman rank-order correlation coefficient
Nominal (two levels) Within-groups Are two groups different? Wilcoxon signed-rank test
Nominal (two levels) Between-groups Are two groups different? Mann–Whitney U test
Nominal (three or more levels) Between-groups Are three or more groups different? Kruskal–Wallis H test
Table : TABLE E.5 Nonparametric Statistics and Their Parametric Counterparts Every parametric hypothesis test has at least one nonparametric counterpart. If the data are far from meeting the assumptions for a parametric test or at least one variable is ordinal, we should use the appropriate nonparametric test instead of a parametric test.
Design Parametric Test Nonparametric Test
Association between two variables Pearson correlation coefficient Spearman rank-order correlation coefficient
Two groups; within-groups design Paired-samples t test Wilcoxon signed-rank test
Two groups; between-groups design Independent-samples t test Mann–Whitney U test
More than two groups; between-groups design One-way between-groups ANOVA Kruskal–Wallis H test

The decisions we’ve outlined are summarized in Figure E-1.

Figure E-1

Choosing the Appropriate Hypothesis Test By asking the right questions about our variables and research design, we can choose the appropriate hypothesis test for our research.

E-3

E-4