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Thread: measure of effect size for categorical association

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    measure of effect size for categorical association


    I am having difficulties in wrapping my head around an issue regarding chi-squared statistic, Cramer's V, and Cohen's measure of effect size.

    At the best of my understanding, chi-square statistic does not convey any idea on the strength of association between rows and columns of a contigency table since chi-square statistic is dependent on the size of the table (i.e., the table's grand total).

    To put it more formally, quoting from Sheskin's Handbook of Parametric and Nonparametric Statistical Procedures:
    The reason why a chi-square value computed for a contingency table is not an accurate index of the degree of association between the two variables is because the chi-square value is a function of both the total sample size and the proportion of observations in each of the r c cells of the table. The degree of association, on the other hand, is independent of the total sample size, and is only a function of the cell proportions. In point of fact, the magnitude of the computed chi-square statistic is directly proportional to the total sample size employed in a study.
    That's why measures of (categorical) associations are used, like for instance Pearson's phi, Cramer's V, and the like.
    Quoting from Sheskin:
    A number of different measures of association/correlation that are independent of sample size can be employed as indices of the magnitude of a treatment effect for an r c contingency table.
    In the same book, for each coefficient, the Author also takes into account Cohen's effect size measures. For example, for Cramer's V, Cohen's measure of effect size (namely, w) can be calculated as:
    w=Cramer'sV * squareroot(k-1)
    where k is the number of rows or columns, whichever is smaller.

    Finally, my question:
    if Pearson's phi or Cramer's V can be considered measures of effect size (can they?), why should we derive another such measure from them (i.e., w in this case)?

    Hope this makes sense.
    Thanks for any insight into the issue.


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    Re: measure of effect size for categorical association

    Not familiar with "w". Is Cramer's V a bounded effect sized between 0-1?

    For small tables you all have the option of odds ratios, relative risks, or differences I would imagine.
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