Median Dichotomization in CFA: Is That Allowed?

Configural Frequency Analysis began life as a way to find types in data measured on a nominal scale. Researchers wanted to use it on data that carried more information than that, at least ordinal measurements, and the fix that got proposed was to break such data into discrete categories before running the analysis. The specific recipe that caught on was median dichotomization: split each variable at its median into two groups. In practice almost nobody uses anything else.

Cutting a continuous or ordinal variable in half throws information away, and most people who work with CFA already know this. They accept that the cost is some loss of efficiency. The point raised here is that the damage goes further than a drop in efficiency. Dichotomizing at the median can manufacture interactions that were never there in the untouched data.

That has a consequence for the decisions CFA produces. It is understood that splitting at the median can hide real types, so the analysis fails to flag something that genuinely exists. Those are the conservative errors. But the spurious interactions pull in the opposite direction too. The procedure can point to a type that has no basis in the original data, which is a non-conservative error. So the same simplification that makes users miss real structure can also make them see structure that isn't there.

Joachim Krauth, Department of Experimental Psychology, University of Düsseldorf.