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I have two groups (control and experimental) with 16 subjects each. Their pre-test scores are statistically different from a normal distribution so I opted to do nonparametric tests. I need to compare the learning gains of the students (post test score minus pre test score) but don't know what nonparametric test to use. I know though that if I were to use parametric tests, the ANCOVA is the test that I should use. What is ANCOVA's nonparametric test counterpart?

EDIT: Can I use Quade's test for this? This is a quasi-experimental study by the way, with the objective of determining whether a learning intervention enhance student achievement.

Thanks in advance!

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  • $\begingroup$ You do not need to have normally distributed data to apply an ANCOVA. Use the "asymptotic chi-square" test instead of the F-test. $\endgroup$
    – AdamO
    Commented Mar 9, 2018 at 14:11
  • $\begingroup$ The goal of ANCOVA is to account for variability caused by covariates. Do you have covariates? $\endgroup$
    – Dave
    Commented Nov 18, 2019 at 11:04
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    $\begingroup$ stats.stackexchange.com/questions/3466/… $\endgroup$ Commented Mar 21, 2020 at 13:45

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If you are willing to subtract the pre-score from the post-score, and consider that your dependent variable, then you can just use a Mann-Whitney test between the two groups.

Otherwise, I think you would have to use an aligned ranks approach to stay in the nonparametric realm.

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  • $\begingroup$ Not sure why you qualified your first statement. Taking the difference between the pre-score and post-score would be the standard approach. $\endgroup$
    – Eli
    Commented Sep 6, 2022 at 13:29
  • $\begingroup$ @Eli , I was thinking that in order to subtract the scores, the observations have to be treated as at least interval in nature. If the observations are treated as ordinal observations, subtraction couldn't be used. But in this case, mixed effects ordinal regression could be used. $\endgroup$ Commented Sep 6, 2022 at 14:45

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