For a large series of \(I\times J\) tables, each containing two observations, the bias of the maximum likelihood estimates of log linear partial association parameters is shown to be equal to the parameters, regardless of the size of I and J. The partial association considered is that between row and column variables; the three way interactions are assumed to be 0. This is a generalization of E. B. Andersen’s results for a series of \(2\times 2\) tables [Conditional inferences for multiple-choice questionaires. J. Math. Stat. Psychol. 26, 31-44 (1973); Conditional inference and models for measuring. Copenhagen (1973)].