ABSTRACT
The bulk of this chapter is based on Rayner and Best (1996a) and Best and Rayner (1996), and considers doubly ordered two-way contingency tables of counts Nij, for i = 1, ... , r and j = 1, ... , c. Initially no row or column totals are assumed to be fixed. In this setting we are interested in Pearson’s product moment correlation for grouped data rP. This correlation is generally thought of as a measure of both independence and linearity between these variables; but see section 10.3. Ultimately we want to consider at least the possibility of more than two random variables. It is then sensible to think of rP as just one of many possible measures of association. In the two-way case, rP reflects the lowest order bivariate moment, assessing how the data differ from what might be expected under the null, independence model in the (1, 1)th moment. Other bivariate moment-based measures of association - or generalised correlations - are available, are readily and practically interpreted, and these may be extended to multi-way tables.
