A Median Split is one method for turning a continuous variable into a categorical one. Essentially, the idea is to find the median of the continuous variable. Any value below the median is put it the category “Low” and every value above it is labeled “High.”

This is a very common practice in many social science fields in which researchers are trained in ANOVA but not Regression. At least that was true when I was in grad school in psychology. And yes, oh so many years ago, I used all these techniques I’m going to tell you not to.

There are problems with median splits. The first is purely logical. When a continuum is categorized, every value above the median, for example, is considered equal. Does it really make sense that a value just above the median is considered the same as values way at the end? And different than values just below the median? Not so much.

So one solution is to split the sample into three groups, not two, then drop the middle group. This at least creates some separation between the two groups. The obvious problem, here though, is you’re losing a third of your sample.

The second problem with categorizing a continuous predictor, regardless of how you do it, is loss of power (Aiken & West, 1991). It’s simply harder to find effects that are really there.

So why is it common practice? Because categorizing continuous variables is the only way to stuff them into an ANOVA, which is the only statistics method researchers in many fields are trained to do.

Rather than force a method that isn’t quite appropriate, it would behoove researchers, and the quality of their research, to learn the general linear model and how ANOVA fits into it. It’s really only a short leap from ANOVA to regression but a necessary one. GLMs can include interactions among continuous and categorical predictors just as ANOVA does.

If left continuous, the GLM would fit a regression line to the effect of that continuous predictor. Categorized, the model will compare the means. It often happens that while the difference in means isn’t significant, the slope is.

Reference: Aiken & West (1991). Multiple Regression: Testing and interpreting interactions.

Gadi says

Hi, what did you do with the observations that were exactly median? Did you categorized them as below or above median (or did you ignore them)?

Dr.STT says

I am facing a problem that if, I have scores of one dependent variable i.e. post achievement scores and pre achievement scores are covariate, and have two independent variable i.e. treatment and gender.

when i chacked the assumption of ANCOVA i.e. homogeneity of regression slopes is violated then can i use Quade Rank ANCOVA

Karen Grace-Martin says

Hi Dr.STT,

Those assumptions are about the inferences you can draw, not about the analysis. I can’t tell you what you should do here without learning much more about your study, but these articles might help:

https://www.theanalysisfactor.com/ancova-assumptions-when-slopes-are-unequal/

https://www.theanalysisfactor.com/assumptions-of-ancova/

https://www.theanalysisfactor.com/model-and-interface-assumptions-and-data-issues-differences/

Kristen says

Hey, I calculated an ANOVA using median splits and got significant results (interaction and main effects). However, calculating the same with continuous variables, only the main effect remains significant. How can this be, when the ANOVA has less power? Do you have any idea?

Karen Grace-Martin says

Hi Kristen,

It’s possible that the relationship between continuous X and Y isn’t linear. Maybe it curves.

Alan pagsuyuin says

how do we compute for median split and can we test mediation with median split results? thanks

sam says

Is it possible to use the mode value to split the data instead of the median?

Karen Grace-Martin says

You generally don’t want to use any arbitrary value to split the data. There has to be a qualitatively meaningful difference between the two groups.

Pascal says

Hello, could you point me to a published source concerning the first point that was made? I only found the the post by Vanderbilt University.

I appreciate your help.