Question

10. Tukey's HSD test Aa 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 aggressive behavior. They study nine children without sleep apnea, nine children with untreated sleep apnea, and nine 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 Untreated Sleep Apnea Treated Sleep Apnea 0.27 0.54 0.32 0.1568 0.2592 0.1800 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 Variation Between Treatments Within Treatments Total Degrees of FreedomMean Square Sum of Squares 0.3714 0.5960 0.9674 0.1857 7.49 24 0.0248 26 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 q at a 01. The q value for this problem is The Studentized Range Statistic (q) Error Term 20 2.95 3.58 4.02 4.64 2.92 3.53 3.96 4.55 2.89 3.89 4.45 2.86 3.44 3.82 4.37 2.83 3.76 4.28 24 30 3.49 40 60 3.40 Now, use the q value to calculate Tukey's HSD Tukey's HSD is between any two samples must be at least to be significant. Thus, the mean difference The top value is a-,05; the bottom (bold) value is a-01. The number of treatments is listed across. The df for the error term is in the left column, whene the nomor term, is ฮnother name for the within-tratments variance The researchers conclude that the population means for children without sleep apnea and children with untreated sleep apnea differ They differ conclude that the population means for children without sleep apnea and children with treated sleep apnea They apnea differ conclude that the population means for children with untreated sleep apnea and children with treated sleep

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Answer 1

Giuen thal, Heve h ANOVA table is giuen as Sum ‘f variation edom (d Mean Sp-ar Between -4+9 Trealmenks0.314 Within Treatmens059G0 o-185 realments 0.0249 Total 0.9674 20 eve msthin ratment) alpha (x) o.o from Studetiyed Rae statiste Gitical Q table 3.53 0.0848 = 3.53 x

3.53 x 0.0585 0.1353 ukeqs HSD0.1853 90, Henc theve ane tee paixs alS Ne Sleep - untreated Eleep (mean dliflerence) 0.2구-0.54 = -0.9 2 0.1853 S0, Reseerchers Cannot Co that e population means childrenwuithout sleep apnea and childre uHh m treated sleep apnea difer

eep- Trealed slee rican dierence 0.27.-0.32 So, Researchers Cannot Conckvde peplation means fo children without &leep apnea and children uoith theated Sleep apnea differ Unteated sleep -Treated sleep Mean di erence 0.54-0.32 - Treated Slee = 0.22 〉 0.1853 Sochers o Conclude hat tHe Populat means children with unhrealed Sleep apnea and childwith teated Sleep a Can Conclu apnea der.