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Is it possible to transform my variables to their ranks and apply MANCOVA to the transformed data, just like how it is done in rank ANCOVA?

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  • $\begingroup$ State your goal and perhaps give an example setup specifying some independent and some dependent variables. $\endgroup$ – Frank Harrell Jan 4 '16 at 12:56
  • $\begingroup$ (Example adapted from "The Analysis of Covariance and Alternatives") Suppose we have two dependent variables in an achievement study - scores on an achievement test of mathematics and scores measuring interest in mathematics. The independent variable is the type of training that the subjects underwent (3 in this case) and the covariate is a measure of aptitude. Our goal is to test whether the three adjusted population centroids are equal. It seems that MANCOVA can be used in this example. However, I am wondering what we can do if our data violate the normality assumptions of MANCOVA. $\endgroup$ – statsmajor Jan 4 '16 at 14:56
  • $\begingroup$ "in R" seems a distraction here: suggest that you remove it. $\endgroup$ – Nick Cox Jan 4 '16 at 16:12
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In this case Peter O'Brien's method of turning the problem around makes sense. Use a polytomous logistic regression model to estimate the joint relationship between the two dependent variables and the probability of being assigned to each of the three training methods. This makes no distributional assumptions. You can relax assumptions that are akin to the equal covariance matrix assumption by including nonlinear terms on the right hand side of the model. See http://www.citeulike.org/user/harrelfe/article/13264639

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