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Suppose I have the following experiment set up. I'm trying to build a regression model to predict how much weight a person can bicep curl based on their bicep size. So I go ahead and have a bunch of people lift some weight, measure their bicep size and fit a regression model to the data.

Now I calculate the difference between the actual weight they lifted and the predicted weight and notice (visually)that there is a trend for my model to overestimate how much someone with a small bicep can lift (negative errors), normal biceps seem to be pretty accurate predictions and it overestimates how much someone with a large bicep can lift (positive errors).

How would I go about doing the equivalent of a one sample t-test if I violate the assumption of homogeneity?

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EDIT: Will multiple Wilcoxon signed rank test with alpha correction be appropriate here?

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    $\begingroup$ Although it's not your question, a better way to proceed here is to think about working on square root or logarithmic scale. In any case (1) why isn't bicep size measured? (2) as you have three groups so far as I can see, why is a t test relevant at all? $\endgroup$
    – Nick Cox
    Apr 20 '20 at 10:31
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    $\begingroup$ Naturally I know nothing of the context, but advice very often repeated here is that categorizing continuous predictors is almost always a bad idea statistically. stats.stackexchange.com/questions/16565/… for example gives advice wider than the post title implies. $\endgroup$
    – Nick Cox
    Apr 20 '20 at 11:06
  • $\begingroup$ 1) In this particular case it would be useful to think of the categorizing of bicep size as something akin to bmi. It's useful in the sense that it provided theoretical bins used for a particular purpose. 2) I was an idiot and forgot about the one sample Wilcoxon signed rank test. Will multiple Wilcoxon signed rank test with alpha correction be appropriate here? $\endgroup$ Apr 20 '20 at 11:10
  • $\begingroup$ As in my first comment, I see no more grounds for degrading data to ranks any more than I do for categorizing predictors. What regression model are you fitting in any case? $\endgroup$
    – Nick Cox
    Apr 20 '20 at 11:16
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    $\begingroup$ OK, and I appreciate that you're trying to ask a focused question, but I don't think your total approach is very clear in the question. Important details are emerging in the comments, but it's often said that many people don't read comments carefully. $\endgroup$
    – Nick Cox
    Apr 20 '20 at 11:34

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