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**Effect size for the chi-square test for independence**

**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 can be used as a measure of effect size.

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

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

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:

**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.**

Suppose you ask the same question of four times as many people, but the proportions remain the same. The new results are shown in the 2 x 2 data matrix below:

**4. The χ² test statistic for the chi-square test of independence would now be 68.64, and the phi-coefficient would be ________. Thus, when we change the sample size without changing the proportions, the ________ does not change, but the ________ does.**

**5. 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: ________**

**6. According to Cohen's guidelines, the value for the Cramer's V indicates ________ effect.**

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Answered by ChintanPansuriya on coursehero.com

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