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My first question here, hope to be relevant to the community. Im into CS course and a total rookie on statistics, so let me know if more detail is needed and I will edit the post.

I have a problem now that we want to compare sample groups and wanted to come up with a function out of it, so we moved from ANOVA to ANCOVA. The problem now is, the world is not perfect and we do not have a normal distribution of residuals.

This journal suggests few different approaches for ANCOVA. Kurskall Wallis as a non parametric alternative was first considered and then from the journal Quade's non-parametric ANCOVA, and Puri and Sen's non-parametric ANCOVA as well. The 'problem' is that all those three seems to fall under moving all the data to ranks, which seems to lead to loss of inference power.

The question thus are:

  1. Is there to the day any other method that is suggested for not needing to moving the data to ranks while not needing the normal distribution?

  2. Among the 3 (or other you would like to suggest), is there any of them that is more used than the other? And if yes, for which reasons? 2.1 Could you point me to a source that show their assumptions and constraints? Im having issues finding a book that talks about this on them. It can be a complicated book for a rookie, I don't mind.

  3. I saw a technique called resampling and bootstrapping here, would this be of any use in this specific situation?

  4. Does Chi Square has anything to do with what is intended here?

I know I did not provide any data here, but please assume that what is needed here is what I stated on the title: An ANCOVA for non-normal distributions, if possible (not sure if this is absurd since all I have as background is a very basic statistics course) not moving the data to ranks (if not possible I would appreciate to know why as well).

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There's no need to use a non-parametric approach; this is exactly where to use a generalised linear model. I can't really improve on the wikipedia description:

...the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution.

Take a look at the questions under the generalized-linear-model tag for many examples of their use.

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    $\begingroup$ yes, although depending on goals/aesthetic and philosophical preferences/just how weird the data distribution is, transformation or rank-based approaches or bootstrapping could all be plausible approaches ... $\endgroup$
    – Ben Bolker
    Aug 18 '18 at 21:03

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