I've got a non-normally distributed set of data and would like to run a non-parametric version of an ANCOVA. I've found some good support for using a Kruskal-Wallis for this purpose with a post-hoc Dunn test. The issue I'm running into is if I can add in a covariate and if so, how.
For context, I'm using R and the data looks like the attached sheet.
This does not make the residuals normally distributed, but you could follow van der Waerden (1952, 1953ab, see also the PMCMRplus package in R) and use:
normrank
Sal Mangiafico Covariate is continuous in this case, good question!
Daniel Wright thanks for the advice, I'll look into that!
Hi Connor Esterwood. Would it be sensible and defensible to use the median and IQR for descriptive purposes? If so, you might consider quantile regression.
I often wonder if least absolute deviations regression (rather than OLS) would have become the dominant form of regression, had the computing power we have now been around back when people were first figuring out regression modeling.
Just following on from Bruce Weaver 's point, Farebrother has some nice papers discussing Boscovich's use of least absolute value regression a few decades before Gauss and Legrendre introduced least squares. Here is what I have cited:
@inbook{Farebrother1997,
address = "Hayward, CA",
author = "Farebrother, Richard William",
booktitle = "$L\sb 1$-statistical procedures and related topics",
doi = "10.1214/lnms/1215454135",
editor = "Dodge, Yadolah",
pages = "161--170",
publisher = "Institute of Mathematical Statistics",
series = "Lecture Notes--Monograph Series",
title = "Notes on the early history of elemental set methods",
url = "https://doi.org/10.1214/lnms/1215454135",
volume = "Volume 31",
year = "1997"
}
@book{Farebrother1999,
author="Farebrother, Richard William",
title="Fitting Linear Relationships: A History of the Calculus of Observations 1750--1900",
year="1999",
publisher="Springer",
address="New York, NY",
isbn="978-1-4612-0545-6",
}
The reason I ask is that if the independent variables are all factor (nominal) variables, then you can use Aligned Ranks Transformation Anova as a nonparametric test.
I like the suggestion of quantile regression.
Also, if you search for "robust ancova" you may find an applicable procedure.
However, I was wondering about your phrase "non-normally distributed set of data". Make sure you understand the assumptions of a general linear model. It's not the data that you assume is normal. ( For example, assumptions for general linear models are covered in the following presentation, see slide 8, and then slides 19 - 22.)
https://staff.emu.edu.tr/adhammackieh/Documents/courses/ieng581/lecture-notes/ch03.pdf
Depending on the nature of your dependent variable, a generalized linear model may be appropriate.
Bruce Weaver – I used to wonder if least absolute deviations were not more logical, but they have one drawback. While the least absolute deviations are indeed minimised by the median, just as the least square deviations are minimised by the mean, the proportionate reduction in error is higher with the square deviations, so you get a higher precision model, which is an advantage not to be sneezed at.
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