Question

Imagine we revised a test and, as a result, the true variance became a greater proportion of the total variance. This would mean that the standard deviation of scores of a single person taking the test multiple times would become smaller.

a) True
b) False

Answer 1

The statement is true because an increase in the proportion of true variance to total variance indicates that the scores are more consistent and reliable, leading to a smaller standard deviation of a single person's test scores if taken multiple times.

Step-by-step explanation:

If the true variance of a test score becomes a greater proportion of the total variance, the implication is that the variability due to other sources (like measurement error, grading inconsistencies, etc.) has decreased relative to the true score variance.

This would make the distribution of test scores more reliable, reflecting more accurately the true abilities or knowledge levels of the test-takers. As a result, if a single person were to take the test multiple times, we would expect their scores to be more consistent, thus the standard deviation of their scores would become smaller. Therefore, the statement is True.