Which of the following statements are correct about the phi-coefficient? Check all that apply.
It is a measure of correlation between a dichotomous variable and a continuous variable.
It can be used as a measure of the significance of a relationship between two dichotomous variables.
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:Observed Frequencies
Color Preference
Red Yellow
Female 53 30
Male 20 47
The χ² test statistic for the chi-square test for independence is 17.16. The phi-coefficient is .
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:Observed Frequencies
Color Preference
Red Yellow
Female 212 120
Male 80 188
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.
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 200 respondents into four categories: male child, female child, male adult, and female adult. You also decide to look at differences in preferences for three (3) colors: red, blue, and yellow. The χ² test statistic for the chi-square test of independence is 3.31, and Cramer’s V would be .
According to Cohen’s guidelines, the value for the Cramer’s V indicates effect.
