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8. Tukey's HSD test A Aa Sleep apnea is a disorder characterized by pauses in breathing during sleep. 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 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 inattentive 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. Inattentiveness 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 No Sleep Apnea Untreated Sleep Apnea Treated Sleep Apnea Sample Mean Sum of Squares 0.53 0.5780 0.71 0.7220 0.68 0.6480 The researchers perform an analysis of variance (ANOVA) at a = .05 to test the hypothesis that the treatment means are equal. The results are presented in the following ANOVA table. ANOVA Table Source of Variation Sum of Squares Degrees of Freedom Mean Square Between Treatments Within Treatments 0.3906 1.9480 0.1953 0.0325 60 Total 2.3386 The Studentized Range Statistic (9) The ANOVA yielded a significant F statistic, so the null hypothesis is rejected. Since there are more than two groups, the researchers are interested in determining which groups are different. The Tukey's Honestly significant difference (HSD) test will be used to evaluate the pairs. First, use the table at the right to determine the appropriate value of at a 05. The value for this problem is Now, use the value to calculate Tukey's HSD. Tuker's so is Thus, the mean difference between ages must be at least conclude that the population means for children without sleep apnea and children with untreated conclude that the population means for children without sleep apnea and children with treated sleep apnea conclude that the population means for children with untreated sleep apnea and chdren with treated sleep

Answer 1

Ans: =) No. of treatments (k) = 3 Usong table the critical value of q for of the 116 60 95 13.40) -) from table, MSE = 0.0325 I Tukey's ASD = q MSE ( + + + 2) = 3.40 / 00325 (+1) - 3.40 0.0325 # (6.1338) mean difference between amy must be at least 0.138 to be thes, the two Samples Significant. Comparison - Difference 0.53-0.71 = 0.71 0.68 = 0.18 0.03 0.53 0.68 = 0.15 - - - 4th blank - 5th blank - 6th blank - can Can not can