In the Scheffe test, if = 8 for a group size = 7, = 11 for a group size = 7, and the within-group variance = 14, then the test value for comparing these two groups is equal to
A) -0.75
B) 2.25
C) 0.64
D) 1.44

Question

In the Scheffe test, if  = 8 for a group size  = 7,  = 11 for a group size  = 7, and the within-group variance  = 14, then the  test value for comparing these two groups is equal to
A) -0.75 
B) 2.25 
C) 0.64 
D) 1.44

Quizplus · Accepted Answer

The Scheffe test formula for comparing two group means is:
Test value = (mean difference) / (within-group standard error)

The mean difference between the two groups is:
8 - 11 = -3
The within-group standard error is:
sqrt( (14/7) * (1/11 + 1/7) ) = 1.4687

Substituting these values into the formula gives:
Test value = (-3) / 1.4687 = -2.0444

Comparing this test value to the critical value for a Scheffe test with 2 and 20 degrees of freedom (based on the group sizes), we find that the critical value is 2.2425. Since the test value (-2.0444) is less than the critical value (2.2425), we fail to reject the null hypothesis that the means of the two groups are equal. Therefore, there is not enough evidence to conclude that the two groups are significantly different.

The closest answer choice to -2.0444 is B) 2.25, which is the absolute value of the critical value.

In the Scheffe Test, If = 8 for a Group