Question 12.4: Using the Tukey test, test each pair of means in Example 12–......
Using the Tukey test, test each pair of means in Example 12–2 to see whether a specific difference exists, at 𝛼 = 0.05.
a. For \bar{X}_{1} versus \bar{X}_{2}
q=\frac{\bar{X}_{1}-\bar{X}_{2}}{\sqrt{s_{W}^{2} / n}}=\frac{66.8-43.5}{\sqrt{274.33 / 6}}=3.446
b. For \bar{X}_{1} versus \bar{X}_{3},
q=\frac{\bar{X}_{1}-\bar{X}_{3}}{\sqrt{s_{W}^{2} / n}}=\frac{66.8-69.2}{\sqrt{274.33 / 6}}=-0.355
c. For \bar{X}_{2} versus \bar{X}_{3},
q=\frac{\bar{X}_{2}-\bar{X}_{3}}{\sqrt{s_{W}^{2} / n}}=\frac{43.5-69.2}{\sqrt{274.33 / 6}}=-3.801
To find the critical value for the Tukey test, use Table N in Appendix A. The number of means k is found in the row at the top, and the degrees of freedom for s_{W}^{2} are found in the left column (denoted by ν ). Since k=3, d.f. =18-3=15, and \alpha=0.05, the critical value is 3.67. See Figure 12-3. Hence, the only q value that is greater in absolute value than the critical value is the one for the difference between \bar{X}_{2} and \bar{X}_{3}. The conclusion, then, is that there is a significant difference in means for the Houston buildings and the New York City buildings.
