10. Tukey\'s HSD test Aa Aa Sleep apnea is a disorder characterized by pauses in

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 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 Group No Sleep Apnea Untreated Sleep Apnea Treated Sleep Apnea Sample Mean Sum of Squares 0.59 0.45 0.31 0.3240 0.4410 0.2250 The researchers perform an analysis of variance (ANOVA) at = .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 Between Treatments Within Treatments Tota Degrees of Freedom Sum of Squares 0.4312 0.9900 1.4212 Mean Square 0.2156 0.0330 6.53 32

Explanation / Answer

Here as the ANOVA table is given

Here MS (Withing treatment) = MSW = 0.0330

number of observation per treatment = 11

so for dF = 30 , k = 3 annd alpha = 0.05

Critical Q value from studentized Range statistic table (q) = 3.49

Tukey' s HSD = q * sqrt [MSW/n] = 3.49 * sqrt[ 0.0330/ 11] = 0.1912

so, Here there are three pairs .

(i) No sleep - Untreated sleep (mean difference) = 0.59 - 0.45 = 0.14 < 0.1912

so Researchers cannot conclude that the population means for children without sleep apnea and children with untreated sleep apnea differ.

(ii) Untreated sleep - Treated sleep (Mean difference) = 0.59 - 0.31 = 0.28 > 0.1912

Researchers can conclude that the population means for children without sleep apnea and children with treated sleep apnea differ.

(iii) Untreated sleep - treated sleep (Mean difference) = 0.45 - 0.31 = 0.14 < 0.1912

Researchers cannot conclude that the population means for children with untreated sleep apnea and children with treated sleep apnea differ.

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