Question

11. Effect size for the chi-square test for independence Aa Aa Which of the following statements are correct about the phi-coefficient? Check all that apply. It is determined only by the proportions in a 2 x 2 data matrix. It is the same as Cramer's V when the data are a 2 x 2 matrix. It can be used as a measure of the significance of a relationship between two dichotomous variables. * It can be used as a measure of the strength of a relationship between two dichotomous variables. Suppose you are looking at the relationship between gender and color preference. You wonder if there is a difference between the preferences of males and females for red and yellow. You conduct a quick survey asking different people which color they prefer. The results are shown in the 2 x 2 data matrix below: Observed Frequencies Color Preference Red Yellow 53 30 20 47 Female Male The X2 test statistic for the chi-square test for independence is 17.16. The phi-coefficient is According to Cohen's guidelines, the value for the phi-coefficient indicates effect.

Answer 1

all that apply:

• It is the same as Cramer's V when the data are a 2 x 2 matrix.
• It can be used as a measure of the strength of a relationship between two dichotomous variables.

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Phi coefficient, ϕ = √(χ²/N) = √ (17.16 / 150) = 0.34

According to Cohen's guidelines, the value for the phi-coefficient indicates strong effect.

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Phi coefficient, ϕ = √(χ²/N) = √ (51.48 / 450) = 0.34

Thus, when we change the sample size without changing the proportions, the strength of the association does not change, but the significance of the association does.

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df = (r-1)(c-1) = (4-1)(6-1) = 15

Cramer's V = √(χ²/(N*min(r-1, c-1))) = √( 8.81 /(250*3)) = 0.1084

Cramer's V indicates moderate effect.