A Tukey interval for two varieties

Topic: Analysis of variance · more questions on this topic
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Five corn varieties are grown in r=3 plots each. The variety means include \overline y_3=59.800 and \overline y_4=48.300. The residual mean square on 10 degrees of freedom is 10.57. The studentised-range quantile Q_{5,10;\,0.95} is 4.654.

Compute the Tukey interval for \mu_3-\mu_4 at familywise level 0.05, and say whether the test declares the two means different.

Worked answer (click to show)

The estimated difference is 59.800-48.300=11.5. The half-width is

4.654\sqrt{\frac{10.57}{3}}=4.654\times1.877\approx 8.74.

The interval is 11.5\pm 8.74, that is (2.76,\,20.24). It excludes zero, so the two variety means are declared different at familywise level 0.05.