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I'm using Friedman's nonparametric tests for repeated measures for my thesis (I tried transformations on all variables first but data was still highly skewed) and had 2 questions:

  1. What are the best descriptive stats to put in a table. Means and SDs are commonly reported but Friedman's tests use rank ordering of the means. Should I report median values and range? I read somewhere that this is more appropriate but I've never really seen it done in empirical papers. Or is it better to report mean, SDs and medians?

  2. Second question is what statistics to plot in a graph. I had means with standard error bars but I'm also not sure if this is ok, given the use of nonparametric tests. A previous post said confidence intervals can be used instead of standard error bars with median values, but I'd really just like to know if it's ok to use a graph with means and SDs when your analysis contains nonparametric tests, or whether this is totally unacceptable.

Thanks in advance for any advice anyone can provide!

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  • $\begingroup$ This question is answered elsewhere on the site. See especially comments about the good value of Hodges-Lehmann estimators. $\endgroup$ – Frank Harrell Oct 11 '11 at 13:41
  • $\begingroup$ @clairec What kind of variable is your dependent variable? How discrete is it? $\endgroup$ – Jeromy Anglim Oct 11 '11 at 22:06
  • $\begingroup$ @Jeromy, in response to your earlier question, for some of the nonparemtric tests the dependent variable is discrete ie. scores out of 20 on a test and for some it is continuous $\endgroup$ – clairec Oct 12 '11 at 2:05
  • $\begingroup$ @clairec the reason I ask is that for data with a lot of tied ranks as is common in some single item measures and counts with a lot of zeros and ones, the median can lack the nuance of some other statistics. $\endgroup$ – Jeromy Anglim Oct 12 '11 at 8:01
  • $\begingroup$ I failed to note the "Friedman" with "nonparametric" so the Hodges-Lehmann estimator may not apply. But Friedman's test has low power in some cases. $\endgroup$ – Frank Harrell Oct 12 '11 at 11:52
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You can almost never go wrong with more information. With that in mind, reporting the median, interquartile range and range is a good idea. Also, reporting the bootstrapped 95% CI of the median is also a good idea. (See Haukoos JS, Lewis RJ. Advanced Statistics: Bootstrapping Confidence Intervals for Statistics with ‘‘Difficult’’ Distributions. Academic Emergency Medicine 2005;12:360-5 for more information.)

SEM is rarely appropriate for graphs, as it speaks to the population, not to the sample. I think it is totally acceptable for the graphs to have SDs plotted. That being said, you'll get many different opinions about this, as there is no "best practice". Just be sure that the caption to your graph is completely descriptive of what is contained within the graph, and you'll be fine!

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This largely overlaps with what @propofol has said.

Example reports

  • You might get additional inspiration by doing a search on Google Scholar specifically for "Friedman's test". However, I admit that when I had a quick look a fair few studies were not implementing best practice in reporting.
  • One interesting example is Blana et al (2006, PDF HERE). They graphically represented the change using box plots for each time point (i.e., showing median, interquartile range, outliers, and so forth). I think this is a good option.

Blana, A., Rogenhofer, S., Ganzer, R., Wild, P., Wieland, W., and Walter, B. (2006). Morbidity associated with repeated transrectal high-intensity focused ultrasound treatment of localized prostate cancer. World journal of urology, 24(5):585-590.

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