Question

Alisha is conducting a paired differences test for a "before (B score) and after (A score)" situation. She is interested in testing whether the average of the "before" scores is higher than that of the "after" scores.

(a) To use a right-tailed test, how should Alisha construct the differences between the "before" and "after" scores?
(b) To use a left-tailed test, how should she construct the differences between the "before" and "after" scores?

Answer 1

Explanation:

The question says that Alisha is interested in testing whether the average (mean) of the B scores is GREATER THAN the average of the A scores.

Normally, a right-tailed test is used to conduct such experiment because Alisha is comparing in the positive - greater than.

Since we weren't given any figures in the question, we'll use algebra.

Hence,

Let the mean of the B scores be X

and the mean of the A scores be Y

(A) In this case, Alisha wants to know if X is greater than Y. She'll construct the difference between both means thus:

Null hypothesis: X is greater than Y

Alternative hypothesis: X is not greater than Y

Remember that the null hypothesis is the fact which the researcher is testing or which he/she wants to ascertain or prove WHILE the alternative hypothesis is the negating event.

(B) For a left-tailed test to be conducted, Alisha's research statement will be rephrased thus:

Alisha is interested in testing whether the average of the A scores is LESS THAN the average of the B scores.

The hypothesis statement will now be:

Null hypothesis: Y is less than X

Alternative hypothesis: Y is not less than X

As the distinction between both types of hypothesis test has been established, in each case, succeeding statistical-analysis steps are the same.

Alisha can then perform her regression analysis with the numerical data given.