b. Tubby's multiple comparison method Sleep apride is a disorder characterized by pauses in breathing during shop. Children who suffer from untreated sleep apnea often have behavior problems, including hyperactivity, inattention, and aggression. A common treatment for pediatric sleep apnea is the surgical removal of enlarged Bevisits and adenoids that and ubritructing the airmays. Suppose researchers at a sleep clinic and interested in the effect of surgical treatrant for podiatric slep apnea on hyperactive behavior. Thay study 21 children without sleep apnea, 21 children with untreated sleep apnea, and 21 children who have bian surgically treated for slip apria. Hyperactivity is measured using the Conners Rating Scalia. 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 0.41 0.5120 Untreated Sloop Apnea 0.72 0.8820 Treated Skop Aprica 0.48 0.7230 The researchers perform an analysis of variance (ANOVA] at a = 0.01 to test the hypothesis that the treatment means are equal. The results are prisainted in the following ANOVA table ANDVA Tabia Source of Variation Sum of Squirm Dugriss of Freedom Mean Square 1.1 2 0.56 1400 Error 2.12 60 0.04 Total 3.23 The mall trypothesis of equal treatment means is rejected, so at least two treatment means difer. The researchers use Tukay's multiple comparison method at a = 0.01 be delermine which of the treatment means differ. Critical Values of the Studentized Range LST The lop values are for a = .05; the bottom (bold) valuin are for a = .01. As in your text, b deroles the columns and v denotes the roms of that Labke. Use Tuking's multiple comparison method at a = 0.01. Use the table to the left to find the critical value of the Studentiand range q (kv]. qu(k, v) = The critical number u = The researdri T conclude that the population madre for children without shep apnea and children with untreated slip apria differ. Thiry T conclude that the population madre for children without slep apnea and children with treated shoop apnea differ. They 7 conclude that the population means for children with untreated shop apria and children with treated shop apnea differ