11. The Scheffe test Aa Aa Sleep apnea is a sleep disorder characterized by paus
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11. The Scheffe test Aa Aa Sleep apnea is a sleep disorder characterized by pauses in breathing during sleep. Children with sleep apnea have behavior problems, induding hyperactivity, inattention, and aggression, as well as impaired learning and diminished academic performance. The removal of tonsils and adenoids that are enlarged, causing the obstruction of the airways, is one of the most common treatments for pediatric sleep apnea. A clinical psychologist studies the effects of tonsillectomy and adenoidectomy on inattentive behavior. Her quasi-experiment indudes three groups of 11 children. The first group of children does not have sleep apnea, the second group has untreated sleep apnea, and the third group has sleep apnea treated by tonsillectomies and adenoidectomies. Inattentiveness was measured using parent reports on the Conners Rating Scale. The sample means and sums of squared deviations of the s“res for each of the three groups are presented in the table that follows. Group Sample Mean Sum of Squares 0.60 0.45 0.3 0.3240 0.4410 0.2250 No sleep apnea Treated sleep apnea After collecting the data, the dinical psychologist analyzes the data using an ANOVA. The results of her analysis are After collecting the data, the clinical psychologist analyzes the data using an ANOVA. The results of her analysis are presented in the ANOVA table that follows ANOVA Table Degrees of Sum of SquaresFreedomMean Square Source of Variation Between Treatments Within Treatments Total 0.4631 0.9900 1.4531 0.2316 7.02 30 0.0330 32 The cntical value of F when -01 is 5.390, meaning the critical region consists of all F-ratios greater than 5.390. The Fratio is greater than chis critical lyalue, so you know that at least one difference exists among the treatments Since more than two groups are involved, the psychologist is interested in determining which groups are different. The Scheffe test will be used to eveluate the pans Call t no steep spnea group A. the untreated sleep apnea group The Scheffe test will be used to evaluate B, and the treated sleep apnea groupExplanation / Answer
Solution:
No sleep apnea:-0.60*11=6.6
Untreated sleep apnea:-0.45*11=4.95
SSAB=6.6^2+4.95^2/11-11.55^2/22=6.1875-6.06375=0.12375
MSbetween=0.12375/2=0.061875, Fcomparision=0.061875/0.0330=1.875
F is smaller than 5.39 and hence cannot reject the null hypothesis.
No sleep apnea:-0.60*11=6.6
Treated sleep apnea:-0.31*11=3.41
SSAC=6.6^2+3.41^2/11-10.01^2/22=5.0171-4.55455=0.46255
MSbetween=0.46255/2=0.231275, Fcomparision=0.231275/0.0330=7.01
F is greater than 5.39 and hence reject the null hypothesis.
Untreated sleep apnea=0.45*11=4.95
Treated sleep apnea:-0.31*11=3.41
SSBC=4.95^2+3.41^2/11-8.36^2/22=3.2846-3.1768=0.1078
MSbetween=0.1078/2=0.0539, Fcomparision=0.0539/0.0330=1.63
F is smaller than 5.39 and hence cannot reject the null hypothesis.
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