Hi, I am looking for a non-parametric test that is equivalent to ANCOVA.
The DV is measured by a single-item (ordinal variable). My goal is to examine potential group difference in the DV, with the effect of a continuous variable (covariate) being controlled for.
I am not familiar with non-parametric test, and would appreciate if someone can help on this matter. Thank you!
Run the ANCOVA as an ordinal logistic regression. I have some course notes for you. Check out videos on this topic. David Booth
As David Eugene Booth suggested I'd look at ordinal logistic regression. However note that it is a parametric model.
There is some confusion in introductory texts and elsewhere that equate parametric tests/models with assuming a normal distribution (e.g., of residuals). In fact any model that models the parameters of a probability distribution is parametric and that includes logistic and ordinal logistic regression (which use the binomial distribution).
Adding to Thom Baguley's comments about the (very slippery) parametric v non-parametric distinction, note that even the Wilcoxon-Mann-Whitney test (which is generally considered to be one of the classic non-parametric tests) estimates a parameter. See Ronán Michael Conroy's 2012 Stata Journal article for more info. ;-)
Article What Hypotheses do “Nonparametric” Two-Group Tests Actually Test?
It would be interesting to see when some people started using "non-parametric" to mean not assuming some part of the model is normal distributed. Here is what one author said for an influential textbook several decades ago.
the first techniques of inference which appeared were those which made a good many assumptions about the nature of the population from which the scores were drawn, Since population values are `parameters', these statistical techniques are called parametric. \\ \phantom{d} \hfill \citep[p. ~2]{Siegel1956} \\
More recently we have seen the development of a large number of techniques of inference which do not make numerous or stringent assumptions about parameters. These newer `distribution-free' or nonparametric techniques ... \\
\phantom{d} \hfill \citep[p. ~3]{Siegel1956}
So this would suggest "non-parametric" means some specific parameters, but it is not clear where some procedures lie on this definition.
Non-parametric tests are useless relicts from the last century. An alternative to ordinal regression is Beta regression:
https://schmettow.github.io/New_Stats/glm.html#beta-reg
.oO(Damn. It's a pity someone didn't tell Ronán Michael Conroy that rank-based tests are useless 20th century relics before he published his 2005 article in The Stata Journal. Ditto for Fagerland & Sandvik re their 2007 Statistics in Medicine article. Unlike Agresti (1983), they have no excuse, having published in the 21st century.)
- https://www.stata-journal.com/article.html?article=st0253
Article The Wilcoxon-Mann-Whitney test under scrutiny
- https://users.stat.ufl.edu/~aa/articles/agresti_1983.pdf
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