which is true: Assume we have collected three test scores taken on three consecu

Question

which is true:

Assume we have collected three test scores taken on three consecutive days from 10 independent subjects. Restated, each of 10 independent subjects repeats a test over three consecutive days and generates three separate test scores. Now 5 of these subjects gets to listen to music while they take the test while 5 must take the test in total silence. The test scores are recorded for each student. Assuming there is positive covariance between the test scores within each subject and assuming we wish to test for a difference in the mean score for the music group and the mean score of the silent groups which of the following is true?

I. If we assume the scores are independent within subject we will underestimate the standard error of the difference of treatment means.

II. If we assume the scores are independent within subject we will overestimate the standard error of the difference of treatment means.

III. We know that the correct variance covariance structure is the one that reflects compound symmetry.

Explanation / Answer

In this case the correct option is

I. If we assume the scores are independent within subject we will underestimate the standard error of the difference of treatment means.

since if there is positive covariance, then it indicates only positive correlation but we can not estimate whether it is positive association between two groups

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