An individual receives a T score of 73 on a test that measures empathic ability. Taking into account standard error of measurement (SEM), what is his "true score" 68 percent of the time if test-retest reliability is .75?
A) 25 points
B) 10 points
C) 5 points
D) 2.5 points
E) None of these

Question

Quizplus · Accepted Answer

To calculate the "true score" 68 percent of the time, we need to use the formula:
True Score = Observed score + (SEM x z-score)
Where the z-score is the z-score corresponding to the desired confidence level, which in this case is 1 (68% of the normal distribution falls within one standard deviation of the mean).
SEM = Standard deviation of the test scores x sqrt(1 - test-retest reliability)
Assuming that the standard deviation of test scores is 10 (not provided in the question), we can calculate SEM:
SEM = 10 x sqrt(1 - 0.75) = 5
Plugging in the values:
True Score = 73 + (5 x 1) = 78
Therefore, his "true score" 68 percent of the time is 78-73 = 5 points. 
Hence, the correct answer is option C.

An Individual Receives a T Score of 73 on a Test