Question

2.When is Phi appropriate?

3.When Cramer’s V appropriate?

4.What values can phi take on?

Answer 1

2) Phi is a chi-square based measure of association. The chi-square coefficient depends on the strength of the relationship and sample size. Phi eliminates sample size by dividing chi-square by n, the sample size, and taking the square root.Phi is appropriate when we measure the strength of the association between two variables, each of which has only two categories.

3) 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 is appropriate when we measure the strength of the association between one nominal variable with either another nominal variable, or with an ordinal variable. Both of the variables can have more than 2 categories. (It applies to either nominal X nominal, or ordinal X nominal, with no restriction on the number of categories).

4) Computationally, phi is the square root of chi-square divided by n, the sample size: phi = SQRT(X²/n). Generally Phi does not vary from 0 to 1. For tables larger than 2-by-2, the maximum value of phi is the square root of (k - 1), where k is the number or rows or the number of columns, whichever is smaller. This means phi can be greater than 1.0 for larger tables, with a theoretical maximum of infinity, and differs depending on table size.

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). The more unequal the marginals, the more V will be less than 1.0. V can reach 1.0 only when the two variables have equal marginals.