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For my thesis research I have to do Spearman’s correlation tests on a set of ordinal variables. I would like to represent the correlations graphically to include them in the report and give a clearer idea of what is the relationship between the variables. Since the Spearman’s is on ranks, is it most appropriate to make a scatter plot with the ranks or with the actual data? I was also wondering whether it is appropriate to include the graphs with data that do not give significant results, or if only significant ones should be represented.

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  • $\begingroup$ If the variables are indeed ordinal, it means that the steps between levels don't carry known meaning. I can't think of a scenario where you'd want to use the "actual data" in a plot, as numerical differences between ordinal categories are not actually meaningful - if they were, the data would not be ordinal. I'd argue ordinal data can't really be represented as anything but ranks. $\endgroup$ May 4 at 18:41
  • $\begingroup$ > I was also wondering whether it is appropriate to include the graphs with data that do not give significant results... Depends on how you frame it. Ideally for each graph you show, you'd have enough data to say "here's the trend seen in the data AND here's a statistically significant test rejecting the null that this apparent trend is just a fluke / random noise." If your sample's not large enough for statistical significance, it may still be OK to include the graph with an honest description that "this looks like an interesting trend, but we'll need more data to be sure (future work!)" $\endgroup$
    – civilstat
    May 17 at 1:30

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There is a case for both graphs. A scatter plot of ranks shows, as it were, Spearman correlation's view of the data; a scatter plot of the original data shows your view of the data. What might be especially interesting is to show some examples where the relationship is monotonic but strongly nonlinear.

However, a problem could arise with ordinal data where there may be many ties, so you would need to think how to show the frequency of each distinct pair of values directly.

There is scope for a scatter plot matrix or pairs plot to show many plots in one image.

Your question is drifting into territory where only your advisor or supervisor or someone familiar with local rules or styles at your institution can advise on expectations. Further, much depends on how far the readership is expected to be familiar with statistical methods, or (not at all the same thing) how far you are expected to be able to explain the methods you are using, including their strengths and limitations.

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