On the Determination Coefficient in Configuration Frequency Analysis

When analysts work with configuration frequency analysis, they often reach for the determination coefficient to judge how meaningful a particular cell in a frequency table really is. This paper by Jörg Betzin and Peter Bollmann-Sdorra takes that measure apart and looks at how it actually behaves once you put it to work.

Rather than treating the coefficient as a black box, the authors examine several of its properties and trace what happens to it across a range of empirical situations. The behaviour turns out to be less straightforward than casual use might suggest, and that is where much of the discussion concentrates.

Two findings stand out. One is that the coefficient has an upper bound, and that ceiling shifts depending on the dimension of the table you are working with. The other concerns variability: in tables of higher dimension, the coefficient has very little room to move, so its range of possible values becomes quite narrow.

The work connects to familiar statistical territory, including conditional probability and Guttman's lambda, and it is aimed at anyone relying on the determination coefficient to flag which configurations in a contingency table deserve attention.