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I am conducting a study on textrual complexity. We fed people food (3 types) over 3 sessions and asked questions about hunger levels. 20 participants were tested during 60 trials in total. Of the 14 variables, 4 are non-normal and transformation isn't helping. The other variables were tested using the lmer function in R. As an example:

mod1 <- lmer(H1 ~ g + (1|p), data=pdat)

With H1 being hunger levels and G being which food type and p for participant. We used this to look at fixed and random effects, meaning we can look at the main effect of texture differences in activity while taking into account participant differences, etc.

With the remaining 4 variables we are looking at using non-parametric tests (either a Friedman or Kruskal). The data has equal sizes for each variable.

Which of these tests is the best option?

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  • $\begingroup$ Why are you using the other variables separately? As in why are you not including them into your lmer regression? $\endgroup$
    – Shawn Hemelstrand
    Commented Jan 29, 2023 at 1:59
  • $\begingroup$ Because they are not normally distrbuted $\endgroup$
    – luke pringle
    Commented Jan 29, 2023 at 2:09
  • $\begingroup$ Your predictors and outcome do not need to be normally distributed. It is your residuals that should be. See my response in this question: stats.stackexchange.com/questions/602396/… $\endgroup$
    – Shawn Hemelstrand
    Commented Jan 29, 2023 at 2:11
  • $\begingroup$ Would you want to include Session in your model ? $\endgroup$
    – Sal Mangiafico
    Commented Jan 29, 2023 at 2:25

2 Answers 2

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To perhaps answer the question, tests like Friedman or Quade are used for unreplicated complete block design. This design could be modeled with the formula H1 ~ g + (1|p).

You may want to look into models other than Friedman or Quade, like ordinal regression or aligned ranks transformation anova.

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Answer

It seems based off your comments that you are only removing these predictors from the full mixed model because they are non-normal. Yet they seem theoretically relevant to your research question.

Thus, the correct answer to your question is that none of these tests are useful for your purpose, because you are trying to model how these all control for the predicted outcome. Linear mixed models do not assume normality for predictors. They only assume normality of residuals. See the below two citations, which cover what assumptions you need to meet in mixed models.

Citations

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