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Hypothetical scenario. Let's say I'm running 6 separate ANCOVAs. My independent variable in each is field of study (3 groups: science, humanities, and business). For each ANCOVA my dependent variable is a different measure of IQ measured on a continuous scale (e.g., verbal score, math score, reading score, etc). In each ANCOVA there are two covariates: years of education (continuous variable) and sex (categorical variable). Let's say that I'm considering assumptions for each of the 6 ANCOVAs to determine whether running an ANCOVA is appropriate, and let's say that in 4 of the 6 cases I determine that running an ANCOVA is not appropriate: let's say in one instance I violate the homogeneity of regression assumption, in another instance I violate the homoscedasticity assumption (based on looking at plots )of the standardized residuals against the predicted values, in another instance I violate the assumption that the residual are normally distributed for each level of the independent variable, and in a fourth instance I determine based on past literature that my age covariate likely won't be linearly related to my dependent variable at one or more levels of my independent variable. I looked online for a nonparametric test I can run in place of ANCOVA and I found something called Quade's test, and I found some instruction on how to run it in SPSS. However I can't find anywhere online what the assumptions are for the test. So I'm wondering what the assumptions are for Quade's test so I can determine if I can run Quade's test in any or all of the four instances described above in which I violated one of the assumptions for ANCOVA.

Thanks much in advance! FBH

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The Quade test works only for data arranged in unreplicated complete block design. (This is the same as for Friedman's test). It is a rank-based test, but, if my understanding is correct, assumes that the data are at least interval in nature.

There may be more general nonparametric approaches, like aligned ranks transformation anova, that may be appropriate for your situation.

Also, you might investigate if a generalized linear model would be appropriate. For example, for your situation, Gamma regression may be a contender.

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  • $\begingroup$ Thanks for your reply. Yeah, Quade's test doesn't seem appropriate based on what you say. I'll look into the other options you mentioned. $\endgroup$
    – FastBallooningHead
    Commented Mar 5, 2023 at 9:42
  • $\begingroup$ There is also an ancova on ranks, sometimes called Quade ANCOVA, or Quade's method for (nonparametric) ANCOVA. And there are other robust or nonparametric methods for ANCOVA. I'm not very familiar with these, but there are software implementations. $\endgroup$
    – Sal Mangiafico
    Commented Jun 28 at 15:44

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