Ordinal Data and Correlation
Nonparametric hypothesis tests have been developed as replacements for most parametric tests for situations in which there are severe violations of assumptions. We use nonparametric tests primarily (1) when the dependent variable is ordinal and (2) when the data are skewed and the sample is small, in which case we convert scale data to ordinal data. 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.
Nonparametric Hypothesis Tests
The Wilcoxon signed-rank test is the nonparametric parallel of the paired-samples t test. The Mann–Whitney U test is the nonparametric parallel of the independent-samples t test. The Kruskal–Wallis H test is the nonparametric parallel of the one-way between-groups ANOVA. 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. In bootstrapping, we continually sample with replacement from the original sample. This technique allows us to develop a 95% confidence interval from the middle 95% of the means of the many samples.