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I am analyzing a dataset. Each row corresponds to a participant who answered a questionnaire. Each participant is assigned a score based on their answers. I calculated the average score for each regional subgroup and I am interested in a statistical test that would suggest whether some regional subgroup's average score differs significantly from the national average. I am interested in a test whose assumptions regarding the distributions are minimal (for instance, I am not inclined to assume that the distributions are normal). Any suggestions?

By the way, I am working on R.

Thank you!

Max
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  • Are the individual scores available to you? If so, and if you don't want to make any assumption about the distribution, you can use a non-parametric test: https://stats.stackexchange.com/questions/239293/non-parametric-altervative-to-one-sample-t-test – user8463728 Aug 18 '17 at 14:03
  • Wouldn't a test taking into account the distribution of the population mean be better? I should have actually used the term "sample" instead of "population" as we are estimating the population mean based on the sample – Max Aug 18 '17 at 14:17
  • Please correct me if I'm wrong. You are then interested in a 2 sample test, regional sub-group vs the rest, correct?If that is the case, you can use a permutation test – user8463728 Aug 18 '17 at 14:35
  • Well, not exactly. It's regional subgroup + entire sample (i.e. regional subgroup + rest of sample) – Max Aug 18 '17 at 14:58
  • Then you are still ok to use permutation test because regardless of the permutation, you will still have the same population mean. – user8463728 Aug 18 '17 at 15:07
  • It's not the population mean though, it's only the sample mean. So it seems intuitive to me that the test should take into account the distribution around the sample mean, no? – Max Aug 18 '17 at 15:52

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