Given the following information about a test, compute the KR-21 reliability estimate. The test has 20 items, the median is 12, the mode is 14, the mean is 12, and the standard deviation is 3.
A) .33
B) .37
C) .45
D) .49

Question

Quizplus · Accepted Answer

We can use the formula:
KR-21 = (K(K-1)/ (K-1)(Var X)+((M-1)/M)(Var Xi-Var X))/(K + (M-1)(Var Xi-Var X)/(MVar X))
where K is the number of test items, M is the number of test takers, Var X is the variance of the total test scores, and Var Xi is the variance of the ith test item. 
Since we don't have information on the variance of individual items or the number of test takers, we need to make some assumptions. 
Assuming that all the items have the same variance (homogeneity assumption) and that there is only one test taker, we can simplify the formula to:
KR-21 = K(K-1)/(K-1+(Var X/Var Xi))
Using the given information, we can calculate:
Var X = (standard deviation)^2 = 3^2 = 9
Var Xi = s^2 = (mode - median)^2/4 = (14-12)^2/4 = 1
Substituting these values, we get:
KR-21 = 20(20-1)/(20-1 + (9/1)) = 0.49

Given the Following Information About a Test, Compute the KR-21