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I read with the greatest interest: Alternatives to one-way ANOVA for heteroskedastic data

If I want to determine if more than 2 groups are from the same population and I have to deal with unequal sample sizes, unequal variances and non-normal data, can I use the ordinal logistic regression (evaluating the likelihood ratio test)? Why?

(I use R)

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    $\begingroup$ Using ordinal logistic depends on the groups of the outcome (response, target, dependent variable) being ordered. That's what you need to address. As a categorical variable can't be normally distributed and its variance isn't defined, those don't bite. If by "unequal sample sizes" you mean that the groups aren't equally frequent, that will bite largely to the extent that any is rare. $\endgroup$ – Nick Cox Dec 14 '17 at 19:32
  • $\begingroup$ It's not clear in the question what kind of data you have or what you are trying to determine. These probably need to be clarified before anyone can really address the situation you are thinking about. $\endgroup$ – Sal Mangiafico Dec 15 '17 at 1:28
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    $\begingroup$ I'll also caution you about using the language e.g. "if two groups come from the same population" or "from the same distribution". This kind of terminology is used in some text books, and really I think it just sows confusion. This was the same issue that came up in your question about the differences between Kruskal-Wallis and Anderson-Darling. I mean, practically, a t-test isn't really testing if two samples come from the same population. It's really testing if the means of two samples are equal, given some assumptions about their distributions. (continued). $\endgroup$ – Sal Mangiafico Dec 15 '17 at 14:29
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    $\begingroup$ (...cont.). So, it's much better --- whether thinking about statistical tests or when asking questions here --- to be specific as to what kind of data you have and what you are looking to accomplish. For example, in this question, one possibility is that you have a continuous dependent variable and that are you wondering if ordinal regression can be used as a kind of nonparametric alternative to anova (as your introductory link suggests). (Continued). $\endgroup$ – Sal Mangiafico Dec 15 '17 at 14:40
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    $\begingroup$ A second possibility is that you have an ordinal dependent variable and are worried about sample size and variance of the data (as, I think the comment by @NickCox suggests). If leave your questions vague and theoretical, you may get answers, but the answers may not really address the question you think you're asking.... At the end of day, that's my say. $\endgroup$ – Sal Mangiafico Dec 15 '17 at 14:43
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No. The connection between ordinal logistic regression and heteroscedasticity is subtle. The rationale for using ordinal logistic regression is that the probability model for the outcome is a graded response realized by arbitrary ranked thresholds of a latent logistic distribution function. A consequence of this model is that in values predicted close to the referent response level or close to the maximal response level have very low variance.

The purpose of testing in general is not to determine that two groups come from the same population. Statisticians all generally agree the p-value cannot be used as a measure of similarity.

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  • $\begingroup$ Thank you for your answer, it will help hugely my study of ordinal logistic regression $\endgroup$ – statisticianwannabe Dec 14 '17 at 22:12

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