Abstract
The Wilcoxon Matched-Pairs Signed Ranks Test is a nonparametric test that is often viewed as being similar to Student’s t-Test for Matched Pairs, but it is used for ordinal data or data that seriously violate any semblance of normal distribution. Of course, there are many who would argue that it is simply too convenient to compare the Wilcoxon Matched-Pairs Signed Ranks Test to Student’s t-Test for Matched Pairs even though they serve similar purposes. Group differences for when there are two matched pairs are addressed by both tests, but again, the Wilcoxon Matched-Pairs Signed Ranks Test is often used with ordinal data and/or data that are viewed as being nonparametric (with attention to medians) whereas the Student’s t-Test for Matched Pairs is generally used with interval data that rise to the level of parametric distributions (with attention to means). This lesson is interesting in that there is a tied set of values for one of the matched pairs, which introduces some degree of complexity on how values are ranked when there are ties (i.e., for an individual matched pair, there is no difference in the two scores that are being compared).
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Notes
- 1.
As a reminder on the boxplot, the bottom line (i.e., lower hinge) in the box represents the 25th percentile, the middle line represents the 50th percentile (i.e., median), and the top line (i.e., upper hinge) represents the 75th percentile. The whiskers are drawn as horizontal lines that represent data that go beyond values for the 25th percentile (i.e., bottom whisker) and the 75th percentile (i.e., top whisker). Exceptionally divergent data are often represented as small circles that go beyond the whiskers and are typically termed outliers.
- 2.
The density plot provides a graphical summary of density estimates for a given set of data. Density estimation is a data smoothing tool, with inferences made about a population based on provided data.
- 3.
The only exception to this recommendation is to avoid the package name for the few packages made available when R is first downloaded: base, datasets, graphics, grDevices, methods, stats, and utils. Thus, it is common to write mean(SBP) and not base::mean(SBP). However, base::mean(SBP) is perfectly acceptable and produces the same result as mean (SBP).
- 4.
Going back to the prior comment about package names and functions, in this listing of enumerated functions, the base and stats package names have been purposely used to demonstrate their inclusion among the packages available when R is first downloaded.
- 5.
Recall the prior comment that QQ and Q-Q are both used as a proxy for the term Quantile-Quantile.
- 6.
Similar to many other compound words, it is common to see the term(s) scatter plot and scatterplot.
- 7.
By convention, it is not necessary to write stats::functionname() or base::functionname() since the stats package and base package are part of the full set of packages associated with R when it is first downloaded. The formal term stats::wilcox.test is used merely to reinforce the origin (i.e., package) for this function.
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MacFarland, T.W., Yates, J.M. (2016). Wilcoxon Matched-Pairs Signed-Ranks Test. In: Introduction to Nonparametric Statistics for the Biological Sciences Using R. Springer, Cham. https://doi.org/10.1007/978-3-319-30634-6_5
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