A researcher is comparing three groups of the same size. The sample mean of the first group is 11, the sample mean of the second group is 13, and the sample mean of the third group is 15. If the Tukey q-test
Value for comparing group 1 with group 2 is -2.1, then the Tukey q-test value for comparing group 1 with
Group 3 will be:
A) -2.1
B) -4.2
C) -8.4
D) Cannot be determined with the information given

Question

Quizplus · Accepted Answer

The Tukey q-test value for comparing group 1 with group 2 is -2.1, meaning that there is a significant difference between the means of groups 1 and 2. Since group 3 has a higher mean than group 2, it is likely that there is also a significant difference between the means of groups 1 and 3. To find the Tukey q-test value for comparing group 1 with group 3, we need to compare the difference between the means of groups 1 and 3 to the standard error of the difference between the means. The standard error of the difference between the means is equal to:

sqrt[(MSE/n) * (1/a + 1/b)]

Where MSE is the mean square error from the ANOVA, n is the sample size, and a and b are the number of groups being compared. Since we are comparing three groups, a and b are both equal to 3. We do not know the value of MSE or n, so we cannot calculate the standard error directly. However, we know that the Tukey q-test value is equal to the difference between the means divided by the standard error. Since the sample mean of group 1 is 11 and the sample mean of group 3 is 15, the difference between the means is 4. Therefore:

Tukey q-test value = (15 - 11) / SE

We can rearrange this equation to solve for the standard error:

SE = (15 - 11) / Tukey q-test value

Substituting in the given value of -2.1, we get:

SE = (15 - 11) / -2.1
SE = 1.9048

Now that we have the standard error, we can calculate the difference between the means of groups 1 and 3 divided by the standard error:

Tukey q-test value = (15 - 11) / SE
Tukey q-test value = 2.1 * (15 - 11) / sqrt[(MSE/n) * (1/3 + 1/3)]
Tukey q-test value = 4.2

Therefore, the Tukey q-test value for comparing group 1 with group 3 is -4.2. The answer is B.

A Researcher Is Comparing Three Groups of the Same Size