Question

Which of the following statements are correct about the phi-coefficient? Check all that apply. X It can be used as a measure of effect size. It is determined only by the proportions in a 2 x 2 data matrix x 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. 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 green and purple. 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 Green Purple 40 19 35 Male Female The X2 test statistic for the chi-square test for independence is 7.68. The phi-coefficient is 0.25 According to Cohen's guidelines, the value for the phi-coefficient indicates effect. Suppose you ask the same question of twice as many people, but the proportions remain the same. The new results are shown in the 2 x 2 data matrix below: Observed Frequencies Color Preference Green Purple 80 38 52 Male Female 70 The X2 test statistic for the chi-square test for independence would now be 15.36, and the phi-coefficient would be . Thus, when we change the sample size without changing the proportions, the does not change, but the does.

Answer 1

66 54 total 120 c2 32.45 26.55 33.55 27.45 (0--Ei)^2/Ei c1 1.757 2.147 1.699 2.077 TS 7.679 alpha critical value p-value 0.05 3.8415 0.0056

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phi 0.25297

A value of .1 is considered a small effect, .3 a medium effect and .5 a large effect.

This is small effect

b)

52 132 108 38 total 118 122 240 c2 64.90 53.10 67.10 54.90 (0--Ei)^2/Ei c1 3.513 4.294 3.398 4.153 TS 15.358 alpha critical value p-value 0.05 3.8415 0.0001 phi 0.25297

TS = 15.36 , phi is 0.25

phi does not change, but TS changes

cramer's V = sqrt(TS / (n *df))

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

n = 250

TS = 8.81

hence

cramer's V =sqrt(8.81/(250 * 15))= 0.04846