Question

Effect size for the chi-square test for independence

1.Which of the following statements are correct about the phi-coefficient? Check all that apply.

a.It can be used as a measure of the significance of a relationship between two dichotomous variables.

b.It is the same as Cramer’s V when the data are a 2 x 2 matrix.

c.It can be used as a measure of the strength of a relationship between two dichotomous variables.

d.It can be used as a measure of effect size.

e.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
Female	53	30
Male	20	47

2. The χ² test statistic for the chi-square test for independence is 17.16. The phi-coefficient is_________ .

3.According to Cohen’s guidelines, the value for the phi-coefficient indicates ___________ effect.

4. 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
	Red	Yellow
Female	106	60
Male	40	94

5.The χ² test statistic for the chi-square test of independence would now be 34.32, and the phi-coefficient would be_________ . Thus, when we change the sample size without changing the proportions, the ______ does not change, but the __________ does.

6. Now, suppose you conduct a slightly different study. Instead of looking at the difference between the preferences of males and females for two colors, you classify your 250 respondents into four categories: male child, female child, male adult, and female adult. You also decide to look at differences in preferences for five (5) colors: red, yellow, green, blue, and purple. The χ² test statistic for the chi-square test of independence is 99.45, and Cramer’s V would be __________________ .

7. According to Cohen’s guidelines, the value for the Cramer’s V indicates ____________ effect.

Answer 1

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Expected (O, Expected (O, Red red EE,d Yellow YellowE Total 53 40.39333 3.934511730 42.60667 3.7301215 Female5 Male 83 67 150 20 32.60667 4.8740966 73 8.8086084 47 34.39333 4.6208968 77 8.3510183 Total 73

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