Measures of association

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Measures of association

A number of authors have devised measures that seek to indicate the strength of association in two-way classification tables. Some of these measures are only applicable to 2x2 tables, whilst others only apply to tables with the same number of rows and columns (i.e. square tables). In principle, a measure of association should produce a value in the range [-1,1], where 0 is no association, +1 is strong positive association and -1 is strong negative association. In practice the measures do not provide such a convenient scaling. For continuous or interval data standard correlation measures should be used.

Assuming that a chi-square statistic has been computed for a contingency table with r rows, c columns, and overall total of N, the main measures devised are as follows:

Phi index:

Applies to 2x2 tables only. Range [-1,1]

Pearson's contingency coefficient, C:

Applies to tables where r=c=k. Range [-1,1]. The version cited here is adjusted to ensure the range is independent of table size

Cramer's V:

Applies to any table size. Range [-1,1]. If there are only two rows or only two columns the statistic reduces to: