A researcher is comparing three groups of the same size. The sample mean of the first group is 14, the sample mean of the second group is 17, and the sample mean of the third group is 20. If the Scheffé F-test
Value for comparing group 1 with group 2 is 5.4, then the Scheffé F-test value for comparing group 1 with
Group 3 will be:
A) 5.4
B) 10.8
C) 21.6
D) Cannot be determined with the information given

Question

Quizplus · Accepted Answer

The Scheffé F-test compares means of two groups at a time, and the value obtained for comparing group 1 with group 2 does not provide information on the comparison of group 1 with group 3. Therefore, we cannot use the value of 5.4 to directly determine the Scheffé F-test value for comparing group 1 with group 3. However, since the sample mean of group 3 is the highest of the three groups, it is possible that the difference between group 1 and group 3 is larger than the difference between group 1 and group 2. This suggests that the Scheffé F-test value for comparing group 1 with group 3 could be higher than the value of 5.4 obtained for comparing group 1 with group 2. Therefore, the best choice is option C, which is the highest value among the options given.

A Researcher Is Comparing Three Groups of the Same Size