Continuous and Categorical Variables: The Trouble with Median Splits

Stage 2A 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.


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Reader Interactions


  1. 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

  2. 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?

  3. Alan pagsuyuin says

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

  4. 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.

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