Difficulty Factors in Binary Data

A number of writers have regarded difficulty factors as arising from the misbehaviour, in some sense, of correlation coefficients for binary data when the binary variables have varying difficulty levels. McDonald (1965) argued that difficulty factors are due to non‐linear item characteristic curves rather than difficulty per se , but did not give an example using binary data. An artificial experiment is described in which non‐linear item characteristic curves yield a difficulty factor, whereas linear item characteristic curves do not, even when in the latter case the items differ markedly in difficulty and phi coefficients are employed.