6. Tukey's multiple comparison method Sleep apnea is a disorder characterized by pauses in breathing during sleep. Children who suffer from untreated sleep apnea often have behavior problems, including hyperacyity, inattentjonr and aggression. A common treatment for pediatric sleep apnea is the surgical removal of enlarged tonsils and adenoids that are obstructing the airways. Suppose researchers at a sleep clinic are interested in the effect of surgical treatment for pediatric sleep apnea on hyperactive behavior. They study 21 children without sleep apnea, 21 children with untreated sleep apnea, and 21 children who have been surgically treated for sleep apnea. Hyperactivity is measured using the Conners Rating Scales. The sample means and sums of squares of the scores for each of the three groups are presented in the following table. Group Sample Mean Sum of Squares No Sleep Apnea 0.41 0.5120 Untreated Sleep Apnea 0.?2 0.3820 Treated Sleep Apnea 0.48 0.?220 The researchers perform an analysis of variance (ANDVA) at cr = 0.01 to test the hypothesis that the treatment means are equal. The results are presented in the following ANDVA table. MONA Table Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments 1.] l 2 0.56 14.00 Error 2.12 60 0.04 Total 3.23 62 The null hypothesis of equal treatment means is rejected, so at least two treatment means differ. The researchers use Tukey's multiple comparison me'd'lod at c = 0.01 to determine which of the treatlnent means differ. The null hypothesis of equal treatment means is rejected, so at least two treatment means differ. The researchers use Tukev's multiple comparison method at o = 0.01 to determine which of the treatment means differ. Critical Values of the Studentized Range Elf I'Ur Error Term 2 3 20 2.95 3.58 4.02 4.64 24 2.92 3.53 3.95 4.55 30 2.59 3.49 3.59 4-45 40 2.56 3.44 3.32 4.3;" Ell] 2.33 3.40 3.75 4.2?- The top values are for o = .05; the bottom (hold) values are for a = .01. As in your text, k denotes the columns and v denotes the rows ofthe table. Use Tukev's multiple comparison method at c = 0.01. Use the table to the left to nd the critical value of the Studentized range (1,; (km). qn(k,v) = V . The critical numberw = v . The researchers 7 conclude that the population means for children without sleep apnea and children with untreated sleep apnea differ. The.r v conclude that the population means for children without sleep apnea and children with treated sleep apnea differ. The; V conclude that the population means for children with untreated sleep apnea and children with treated sleep apnea differ