Question

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 aggressive behavior. They study 11 children without sleep apnea, 11 children with untreated sleep apnea, and 11 children who have been surgically treated for sleep apnea. Aggression 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 Sample Mean Sum of Squares Group No Sleep Apnea 0.3240 0.59 Untreated Sleep Apnea 0.45 0.4410 Treated Sleep Apnea 0.31 0.2250 The researchers perform an analysis of variance (ANOVA) at α = .01 to test the hypothesis that the treatment means are equal. The results are presented in the following ANOVA table. ANOVA Table Source of Degrees of Sum of Squares Variation Freedom Mean Square 0.4312 0.2156 6.53 Between Treatments Within Treatments 0.9900 0.0330 Total 1.4212 32 The ANOVA yielded a significant F statistic, so the The Studentized Range Statistic (q) null hypothesis is rejected. Since there are more df for Error Term than two groups, the researchers are interested in 2.95 3.58 determining which groups are different. The Tukey's 20 4.02 4.64 Honestly Significant Difference (HSD) test will be 2.92 3.53 used to evaluate the pairs. First, use the table at the 3.96 4.55 right to determine the appropriate value of q at 30 2.893.49 a 3.89 4.45 01. The q value for this problem is 40 2.86 3.44 3.82 4.37 3.40 60 2.83 Now, use the q value to calculate Tukey's HSD 3.76 4.28 Tukey's HSD is . Thus, the mean difference The top value is a.05; the bottom (bold) value is a-.01. The number of between any two samples must be at least treatments is listed across. The df for the error term is in the left column, where to be significant the "error term" is another name for the within-treatments variance. The researchers conclude that the population means for children without sleep apnea and children with untreated sleep apnea differ They conclude that the population means for children without sleep apnea and children with treated sleep apnea differ They conclude that the population means for children with untreated sleep apnea and children with treated sleep apnea differ

Answer 1

q=4.43 ( for number of treatment 3 and error df=30)

tukey HSD=q*sqrt(MSW/n)=4.43*sqrt(0.033/11)=0.2426

difference must be atleast 0.2426 to be significant

comparison		difference	HSD	remarks
without sleep	untreated sleep	0.14	0.2426	non significant
without sleep	treated sleep	0.28	0.2426	significant
untreated sleep	treated sleep	0.14	0.2426	non significant