Illuminating Statistical Analysis Using Scenarios and Simulations

52Other Methods Using Ranks

When data is unruly, using ranks in place of the original scaled data is a good maneuver. And just as the Mann–Whitney–Wilcoxon method uses ranks in place of scaled data and provides an alternative to the -test for mean differences, there are other methods that use ranks and serve as alternatives to other methods we've seen.¹

• Methods to construct confidence intervals for the median (rather than the mean).
• The Kolmogorov–Smirnov test helps determine whether a sample is consistent with a specified distribution and serves as an alternative to the Chi-squared goodness of fit test (Chapters 28 and 30).
• The Kruskal–Wallis method is an extension of the Mann–Whitney–Wilcoxon rank sum method and offers an alternative to one-way ANOVA (Chapter 34).
• Spearman's rank correlation coefficient and Kendall's tau rank correlation coefficient are alternatives to Pearson's correlation coefficient (Chapter 37).

As for alternatives for least-squares regression, often the best bet is to transform the data to another numeric scale or to transform the least-squares criteria itself through use of robust regression methods. These are our next topics.

Notes

1. Methods that use ranks are often referred to as nonparametric methods.