Attempts Average / 6 8. 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 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. It is a measure of correlation between a dichotomous variable and a continuous variable. 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 The x2 test statistic for the chi-square test for independence is 17.16. The phi-coefficient is 0.34 According to Cohen's guidelines, the value for the phi-coefficient indicates a large * effect.Suppose you ask the same question of four times as many people, but the proportions remain the some. The new results are shown in the 2 x 2 data matnx below: Observed Frequencies Color Preference Red Yellow Female 2 12 120 Male so 188 e The )6 test statistic for the chi-square test of independence would now be 68.64. and the phi-coefficient would be V . Thus, sample size without changing the proportions. the 7 does not change, but the 7 does. when we change the 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 ohlld, male adult, and female adult. You also decide to look at differences In preferences for ve (5) colors: red, yellow. green. blue, and purple. The )9 test statistic for the chi-square test of Independence Is 99.45, and Cremer's y would be v According to Cohen's guidelines. the value for the Cramer'l V Indicates V effect. Continue without saving