Which of the following statements are correct about the phi-coefficient? Check all that apply. O It is a measure of correlation between two dichotomous variables. It can be used as a measure of the strength of a relationship between two dichotomous variables. O It is a measure of correlation between a dichotomous variable and a continuous variable. O It can be used as a measure of the significance of a relationship 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 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:

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Which of the following statements are correct about the phi-coefficient? Check all that apply.
It is a measure of correlation between two dichotomous variables.
It can be used as a measure of the strength of a relationship between two dichotomous variables.
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.
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
According to Cohen's guidelines, the value for the phi-coefficient indicates
effect.
Transcribed Image Text:Which of the following statements are correct about the phi-coefficient? Check all that apply. It is a measure of correlation between two dichotomous variables. It can be used as a measure of the strength of a relationship between two dichotomous variables. 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. 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 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 x2 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 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 x² test statistic for the chi-square test of independence is 99.45, and
Cramer's V would be
According to Cohen's guidelines, the value for the Cramer's V indicates
effect.
Transcribed Image Text: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 x2 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 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 x² test statistic for the chi-square test of independence is 99.45, and Cramer's V would be According to Cohen's guidelines, the value for the Cramer's V indicates effect.
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