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Basically, I am comparing outcomes in a variable that applies to everyone in a field to each subcategory of the group (e.g., average annual pay for all nurses versus annual pay for all of the different types of nurses), but I cannot find a test that would be appropriate.

Since I was comparing continuous data for more than two groups, I thought an ANOVA would be appropriate, but the data is non-parametric, so I moved on to a Kruskal Wallis. That is when I realized that since I am comparing the big group to all its subcategories, I am basically comparing a population to a bunch of samples, which I believe would make the relationship dependent. So then I thought of RMANOVA and the Friedman test eventually, but I am unsure whether I can actually do Friedman as I am comparing a population to a sample rather than one group over several instances or several separate dependent groups.

I apologize if this is confusing. I haven't written here before.

kjetil b halvorsen
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A Sani
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  • Data are neither parametric nor nonparametric; models are.

    • See the comments about "nonparametric data" under these questions:

    https://stats.stackexchange.com/questions/351404/coefficient-of-variation-for-nonparametric-data or

    https://stats.stackexchange.com/questions/248094/how-to-interpret-linear-regression-results-in-nonparametric-data (or indeed, comments and or answers under many other such questions). $:$ 2. Is your interest primarily in comparing means across groups?

    – Glen_b Dec 27 '23 at 07:25
  • Yes! I want to compare means. – A Sani Dec 29 '23 at 17:31
  • I see two main options; to make some reasonable distributional assumption (annual pay is likely fairly skewed, perhaps lognormal or gamma would suffice, though possibly there's some need for truncation or something depending on the conditions nurses in this location work under) and test means that way (perhaps via a GLM for example), or to implement a resampling based test of means (such as a permutation test based on the t-statistic, perhaps). A third alternative is to combine the two and base a permutation test on some more suitable statistic for this kind of variable. – Glen_b Dec 30 '23 at 00:22
  • Oh wow, okay. My GLM ended up being very messy, so maybe the other option is the way to go. Thank you! – A Sani Dec 30 '23 at 20:22
  • Messy in a what sense? Using which glm? Is there some unusual aspect to nurses pay? – Glen_b Dec 31 '23 at 04:01
  • @Glen_b: One unusual aspect to nurses pay is that they usually vary much less than pay in other professions – kjetil b halvorsen Jan 11 '24 at 16:28
  • For comparing overall mean to subgroup means see https://stats.stackexchange.com/questions/30562/how-to-test-whether-subgroup-mean-differs-from-overall-group-that-includes-the, https://stats.stackexchange.com/questions/134627/compare-means-of-group-with-a-mean-of-a-subgroup, https://stats.stackexchange.com/questions/116102/compare-group-mean-to-larger-group-of-which-it-is-part, https://stats.stackexchange.com/questions/83225/testing-whether-the-mean-of-a-group-is-different-from-the-mean-of-the-entire-sam – kjetil b halvorsen Jan 11 '24 at 16:33