Effect size for the chi-square test for independence. Please answer all of the q

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Effect size for the chi-square test for independence. Please answer all of the questions for credit!***

7. 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 can be used as a measure of effect size. 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 is a measure of correlation 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 yellow 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 Yellow Purple Female 89 19 Male 64 The X2 test statistic for the chi-square test for independence is 55.27. The phi-coefficient is options are "A medium "A Large", "No" and "A small" According to Cohen's guidelines, the value for the phi-coefficient indicates effect Hint: When using Cohen's criteria to interpret the phi-coefficient, or Cramer's V, if the value falls between two categories, then the value should be categorized as the smaller of the two categories. For example, a phi-coefficient value of D 23 (with df 1) falls between the small effect and medium effect category, so it should be categorized as a small effect.

Explanation / Answer

Question-7-Options 1,2,3 are correct

For chi-square=55.27 , the phi=sqrt(chi-sqaure/n)=sqrt(55.27/(89+19+28+64))= 0.5257

According to cohen this indicates Large effect

For chi-square=165.81 , the phi=sqrt(chi-sqaure/n)=sqrt(165.81/(267+57+84+192))= 0.5257

Thus, when we change the sample size without changing the proportions, the phi coefficients does not change, but the chi-square test statistic does.

Cramer’s V=sqrt(-chi-sqaure/nt)=sqrt(99.45/(1*250))=0.6307

This indicates large size.

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