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 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. 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 0.42 0.3240 Untreated sleep apnea 0.56 0.4410 Treated sleep apnea 0.30 0.2250 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 0.3729 2 0.1865 5.65 Within Treatments 0.9900 30 0.0330 Total 1.3629 32 The critical value of F when α = 0.05 is 3.316, meaning the critical region consists of all F-ratios greater than 3.316. 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 = 11) and the treatment mean to compute each treatment total (T).) At α = 0.05, the psychologist 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 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 conclude that the population means for children with untreated sleep apnea and children with treated sleep apnea differ.

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 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. 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 0.42 0.3240 Untreated sleep apnea 0.56 0.4410 Treated sleep apnea 0.30 0.2250 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 0.3729 2 0.1865 5.65 Within Treatments 0.9900 30 0.0330 Total 1.3629 32 The critical value of F when α = 0.05 is 3.316, meaning the critical region consists of all F-ratios greater than 3.316. 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 = 11) and the treatment mean to compute each treatment total (T).) At α = 0.05, the psychologist 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 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 conclude that the population means for children with untreated sleep apnea and children with treated sleep apnea differ.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A clinical psychologist studies the effects of tonsillectomy and adenoidectomy on hyperactive behavior. Her quasi-experiment includes 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. 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	0.42	0.3240
Untreated sleep apnea	0.56	0.4410
Treated sleep apnea	0.30	0.2250

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	0.3729	2	0.1865	5.65
Within Treatments	0.9900	30	0.0330
Total	1.3629	32

The critical value of F when α = 0.05 is 3.316, meaning the critical region consists of all F-ratios greater than 3.316. 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 = 11) and the treatment mean to compute each treatment total (T).)

At α = 0.05, the psychologist 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 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 conclude that the population means for children with untreated sleep apnea and children with treated sleep apnea differ.

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