For a study, a chi-square statistic of 1.25 was calculated.There were 40 participants in total, and 2 degrees of freedom for the first variable and 1 degree of freedom for the second variable.What is the effect size?
A) 0.566
B) 0.177
C) 0.125
D) 0.031

Question

Quizplus · Accepted Answer

To calculate the effect size for chi-square, we need to convert the chi-square value to either Cramer's V or phi coefficient. Since we have two degrees of freedom for the first variable, we can use Cramer's V as the effect size measure.

Cramer's V = sqrt(chi-square / (n*(min[c-1, r-1])))

where 
- chi-square = 1.25
- n = 40 (total number of participants)
- c = number of categories for the first variable (unknown)
- r = number of categories for the second variable (unknown)

Since we don't know the exact number of categories for each variable, we can use a conservative estimate of 2 categories for each variable (i.e., min[c-1, r-1] = min[2-1, 2-1] = 1).

Cramer's V = sqrt(1.25 / (40*(1))) = 0.177

Therefore, the effect size is 0.177, which corresponds to choice B.

For a Study, a Chi-Square Statistic of 1