Answered: Sleep apnea is a sleep disorder…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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11. The Scheffe test

Sleep apnea is a sleep disorder characterized by pauses in breathing during sleep. Children with sleep apnea have behavior problems, including 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 hyperactive behavior. Her quasi-experiment includes three groups of 21 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. Hyperactivity was measured using teacher reports on the Conners Rating Scale. The sample means and sums of squared deviations of the scores for each of the three groups are presented in the table that follows.

Group	Sample Mean	Sum of Squares
No sleep apnea	0.41	0.5120
Untreated sleep apnea	0.72	0.8820
Treated sleep apnea	0.48	0.7220

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

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	1.1109	2	0.5555	15.74
Within Treatments	2.1160	60	0.0353
Total	3.2269	62

The critical value of F when α = 0.05 is 3.150, meaning the critical region consists of all F-ratios greater than 3.150. The F-ratio is greater than this critical value, 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 evaluate the pairs. Call the no sleep apnea group A, the untreated sleep apnea group B, and the treated sleep apnea group C.

Start with the calculations you will need to evaluate the difference between the no sleep apnea group (A) and the untreated sleep apnea group (B).

The SSbetween ABbetween AB is _______ .

The FA versus BA versus B is _______ .

(Hint: Recall that you can use the sample size for each treatment (n = 21) and the treatment mean to compute each treatment total (T).)

At α = 0.05, the psychologist CAN OR CANNOT? conclude that the population means for children without sleep apnea and children with untreated sleep apnea differ.

Next evaluate the difference between the no sleep apnea group (A) and the treated sleep apnea group (C). The SSbetween ACbetween AC is ________ . The FA versus CA versus C is _______ .

At α = 0.05, the psychologist CAN OR CANNOT? conclude that the population means for children without sleep apnea and children with treated sleep apnea differ.

Next calculate the values necessary to evaluate the difference between the untreated sleep apnea group (B) and the treated sleep apnea group (C). The SSbetween BCbetween BC is ______ . The FB versus CB versus C is _______ .

At α = 0.05, the psychologist CAN OR CANNOT? conclude that the population means for children with untreated sleep apnea and children with treated sleep apnea differ.

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