3.1 The Tukey Honestly Significant Difference Procedure

The problem with performing inferences on all pairs of means, as we have done above, is that it lends itself to data snooping, i.e., looking for the mean differences that we did not necessarily hypothesize a priori. Tukey's HSD procedure tries to correct for that problem by adjusting critical values for the fact that we are first looking for the biggest observed difference in the analysis. Tukey's procedure is appropriate if you plan to compare all pairs of means. If you only plan to compare a small subset of the pairs, then the Tukey procedure can be overly conservative. To perform Tukey's HSD check off the "Tukey" box under the "Post Hoc Tests for" options in the general linear model procedure.

Task 7.Reportthe Tukey confidence intervals and p-values and compare the Tukey confidence intervals and p-values to the unadjusted ones (LSD). Which confidence intervals are wider?

Multiple Comparisons Dependent Variable: DaysToComplete LSD | Mean Difference 95% Confidence Interval (1) PriorStatus (J) PriorStatus, ( 1-J) Std. Error Sig. Lower Bound Upper Bound above average -8.00' 2.298 002 -12.78 -3.22 below -14.00* 2.404 .000 -19.00 -9.00 average above 8.00' 2.298 .002 3.22 12.78 below -6.00' 2.111 .010 -10.39 -1.61 below above 14.00' 2.404 .000 9.00 19.00 average 6.00* 2.111 010 1.61 10.39 Based on observed means. The error term is Mean Square(Error) = 19.810. *. The mean difference is significant at the .05 level. 0Between-Subjects Factors N PriorStatus, above 6 average 10 below 8 Tests of Between-Subjects Effects Dependent Variable: DaysToComplete Type Ill Sum of Source Squares df Mean Square F Sig. Corrected Model 672.000a 2 336.000 16.962 .000 Intercept 22560.000 22560.000 1138.846 .000 PriorStatus 672.000 2 336.000 16.962 000 Error 416.000 21 19.810 Total 25664.000 24 Corrected Total 1088.000 23 a. R Squared = .618 (Adjusted R Squared = .581)