I am attempting to conduct a Wilcoxon signed-rank test for a within-subject study. My dependent variable is ordinal (Likert scale) and my independent variable consists of two-related groups (same sample questioned at two points in time on their levels of satisfaction).
To conduct the test I created a new variable representing the difference (levels of satisfaction in the past minus levels of satisfaction in the present). To conduct the test one of the assumptions states that the distribution of the differences between the two groups of the independent variable are symmetrical in shape. If this is not symmetrical a transformation is suggested.
However, I do not understand whether I have to transform the two original variables (past levels of satisfaction/ present levels of satisfaction) or the newly created variable representing the difference between the two. The data is ordinal hence never normally distributed, so what transformation can actually be applied?
The assumption about the distribution being symmetric is more nuanced than it appears. Note, first, that it is about the rank differences, not the raw data. But also, I recommend the answer by Alexis here to understand the hypotheses and assumptions of the test: https://stats.stackexchange.com/questions/363335/wilcoxon-signed-rank-test-null-hypothesis-statement/363337#comment683434_363337
Also, note in your case, that this test begins by taking the difference of the values, so that if your data are truly ordinal, you'd have to be treating them as interval in order to be taking this difference.
For truly ordinal data, you could use a two sample sign test.
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