Cramer’s V is a statistic used to measure the strength of association between two nominal variables, and it take values from 0 to 1. Values close to 0 indicate a weak association between the variables and values close to 1 indicate a strong association between the variables.The Cramer’s V statistic is a symmetric measure, in the sense that it does not matter what variable is placed in the rows and what variable is placed in the columns.
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Cramer's V is the most popular of the chi-square-based measures of nominal association because it gives good norming from 0 to 1 regardless of table size, when row marginals equal column marginals. V equals the square root of chi-square divided by sample size, n, times m, which is the smaller of (rows - 1) or (columns - 1): V = SQRT(X2/nm).
Since V has a known sampling distribution it is possible to compute its standard error and significance. SPSS and other major packages report the significance level of the computed V value. The formula for the variance of Cramer's V is given in Liebetrau (1983: 15-16).
Yes, It is possible to use Cramer's V for 3*3 matrix. In simple words, Cramer's V is applicable to all the matrices of 2*2 or more. As this is a method of quantifying strength of relationship, hence minimum 2 variables are required.