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I have two groups of participants and they all took the same measurements.

When I perform a median split on one of the measurements to test my hypothesis about an interaction, the dependent variable fails Levene's test for equality of variances. When I perform a teritary split, it passes Levene's test - both when I am comparing only high and low thirds and when I compare all three thirds too.

There are main effects and interaction effects in all of the ANOVAs that I have run, but only the 2x2 ANOVA fails Levene's test for significance, neither of the 3x2 ANOVAs fail.

How is this possible?

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(1) I really think you should avoid categorizing continuous variables (either dichotomizing, or splitting into thirds). (2) My first guess is that you end up w/ less power w/ the tertiary split, but I'm not sure. – gung Oct 26 '12 at 2:47
I have heard and read arguments for both sides when it comes to categorizing continuous variables, but everyone does it - especially in the social and cognitive sciences. the effects are all significant at least <.01 no matter the split. – user16204 Oct 26 '12 at 2:51
this is a helpful site, especially the main wiki psychwiki.com/wiki/… – user16204 Oct 26 '12 at 2:57
I strongly disagree w/ the information posted there. – gung Oct 26 '12 at 3:03
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I discuss this issue in this answer: how-to-choose-between-anova-and-ancova-in-a-designed-experiment. – gung Oct 26 '12 at 3:23
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1 Answer

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(This isn't a direct answer to the question, more a bunch of references relating to why the approach should be avoided.)

There's a wealth of material on why median (etc) splits of variables are a bad idea.

http://www.uvm.edu/~dhowell/gradstat/psych341/lectures/Factorial2Folder/Median-split.html

http://psych.colorado.edu/~mcclella/MedianSplit/

http://core.ecu.edu/psyc/wuenschk/stathelp/Dichot-Not.doc

MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7, 19–40. here

Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions

http://www.theanalysisfactor.com/continuous-and-categorical-variables-the-trouble-with-median-splits/

Google turns up a bunch more references and links

Cutting in 3 or 4 doesn't avoid the problems.

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