Type Structures in Configural Frequency Analysis

Configural Frequency Analysis, or CFA, is a method for examining data that G.A. Lienert first proposed back in 1969. What sets it apart is how it defines a type in strictly statistical terms. That definition carries a side effect: once you follow it through, you sometimes land on conclusions that feel wrong when you first read them.

The oddity shows up most clearly in small contingency tables. You might expect that any arrangement of cells, any combination of types, antitypes, and cells that are neither, could in principle occur. It turns out that only a slim fraction of those imaginable arrangements can ever actually happen given the statistical rules.

The work here sets out to pin down how slim that fraction really is, offering bounds on the share of type structures that remain possible. From there it considers what those limits mean in practice for anyone running a CFA and interpreting what comes out of it.