Assessing the Strength of Chi Square Statistics

By itself, chi square helps us only to decide whether our variables are independent or related. It does not tell us how strongly they are related. Part of the reason is that the sample size and table size have such an influence upon chi square. Several statistics which adjust for these factors are available. When chi square is thus adjusted it becomes the basis for assessing strength of relationship.

Cramer's V is a measure of the strength of relationship for tables larger than 2 x 2.

V = √ ((chi-square/N) / min (r-1,c-1))

An example:

Consider this table of race by income:

Raw Chi Square = 57.41 with 3 degrees of freedom. Significance = p < 0.00

Cramer's V = 0.153

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Calculations: Chi-square = 57.4 N = 2429

Min [(r-1) or (c-1)] = c-1 = 2-1 = 1

V = √ ((57.4 / 2429) / 1) = 0.153