On the structure of the tetrachoric series

Pearson (1900) introduced the tetrachoric series method for estimating the correlation between two non-measurable characters each with two levels. For characters with more than two levels, Ritchie-Scott (1918) suggested averaging all possible tetrachoric correlations. Using the theory of orthonormal functions, Lancaster & Hamdan (1964) suggested an alternative method essentially based on giving a weighting to each possible tetrachoric table. In this note, a special form of Lancaster & Hamdan's method is used to give an instructive derivation of the tetrachoric series.