Asked by Mitchell Peters on May 07, 2024
Verified
What is the effect size (Cramér's ) for a 3 × 3 table for N = 150 and a chi-square value = 9.49? Use the following formula:
A) .25
B) .06
C) .03
D) .18
Cramér's V
A measure of association between two nominal variables, providing a value between 0 and 1.
Effect Size
A numerical assessment that indicates the size of an occurrence or the intensity of a linkage between factors.
- Acquire the ability to evaluate and determine effect sizes in the context of chi-square tests.
Verified Answer
BA
Bista AbhashMay 11, 2024
Final Answer :
D
Explanation :
To calculate Cramér's phi, we first need to calculate the square root of chi-square divided by N (number of observations):
sqrt(9.49/150) = 0.251
Then we use this value to calculate phi:
phi = sqrt(0.251 / (3-1)) = 0.354
Finally, we divide phi by the square root of the number of rows minus 1 (or the number of columns minus 1, which should be the same for a 3x3 table) to get the effect size:
0.354 / sqrt(2) = 0.250
So the effect size is approximately 0.25, which corresponds to choice D.
sqrt(9.49/150) = 0.251
Then we use this value to calculate phi:
phi = sqrt(0.251 / (3-1)) = 0.354
Finally, we divide phi by the square root of the number of rows minus 1 (or the number of columns minus 1, which should be the same for a 3x3 table) to get the effect size:
0.354 / sqrt(2) = 0.250
So the effect size is approximately 0.25, which corresponds to choice D.
Learning Objectives
- Acquire the ability to evaluate and determine effect sizes in the context of chi-square tests.
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