Is there an alternative interpretation to boxplots for Wilcoxon Sign Test? I compared two variables for repeated measures (say x and y-likert scale 1-7) in Wilcoxon Sign. The boxplot, medians and interquartiles look same in the boxplot (which is normal), but I want to interpret the difference between x and y though, which was still significant. What could be done? There is a mean ranks table (positive, negative etc.) in the SPSS output, but I have not seen a similar visual interpretation referring to these. Many thanks for your suggestions!
Think about what is being tested with the WSR. This is by definition a paired-samples type of test. What is it about the pairs that is being tested?
The net delta (change) per pair is what is being tested. Is the delta net positive, neutral, negative? Is it statistically significant?
Why not display the distribution of delta in a histogram?
The WSR question is: Is the per pair delta statistically significant?
Is delta significant in the aggregate? What are the outliers? Is the distribution uniform? Does the delta in a few pairs drive the overall delta significance?
The default SPSS output for graphic display of the WSR delta is a histogram because it answers all of those questions simultaneously, if you know how to interpret histograms. Consider that Tukey's Boxplot is an iconic (symbolic) representation of the key elements of a distribution (Quartiles Median, Outliers) whereas histograms are the more specific and exact display of distributional data. Both have their uses, and in this case the Boxplot has a far lower level of resolution of horizontal and vertical granularity compared to the histogram. Perhaps an argument could be made for using a density-map to indicate degree of delta as an adjunct to the SPSS WSR histogram, perhaps even an enhancement to it as a color dimension in the display (shading, texture) of the bars in the histogram.
It would be easier to help you if you attached the output from SPSS. But If I understand your request, you could earn additional results in SPSS this way: Analyze -> Nonparametric Tests -> Related Samples. There you have to input variables in "Test Fields" and click "Run". Open your Output window and double click on "Hypothesis Test Summary". Here you get also a graph/chart that visually shows the positive and negative differences between the observations (eg. before and after). If there is a statistically significant difference between x and y, you should see it from this graph as well.
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