Answered: 9. Gravetter/Wallnau/Forzano, - Chapter…

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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9. Gravetter/Wallnau/Forzano, - Chapter 13 - End-of-chapter question 17

The following data are from a repeated-measures study comparing three treatment conditions.

Person	Treatment	Person Totals
I	II	III
A	1	4	7	P = 12
B	4	8	6	P = 18
C	2	7	9	P = 18
D	1	5	6	P = 12
	M = 2	M = 6	M = 7	N = 12
	T = 8	T = 24	T = 28	G = 60
	SS = 6	SS = 10	SS = 6	∑X² = 378

Use a repeated-measures ANOVA with α = .05 to determine whether there are significant mean differences among the three treatments.

Complete the ANOVA table using three decimal places for MS and two for F.

Source of Variation	Sum of Squares	ANOVA Table	Mean Square	F
Degrees of Freedom
Between treatments
Within treatments
Between subjects
Error
Total

F Distribution

Numerator Degrees of Freedom = 6

Denominator Degrees of Freedom = 16

0.01.02.03.04.05.06.07.08.09.010.011.012.0F

Critical value for the F-ratio =

(to three decimal places).

Fail to reject the null hypothesis. There are significant differences among the three treatments.

Reject the null hypothesis. There are no significant differences among the three treatments.

Reject the null hypothesis. There are significant differences among the three treatments.

Fail to reject the null hypothesis. There are no significant differences among the three treatments.

Compute η², the percentage of variance accounted for by the mean differences, to measure the size of the treatment effects:

(to three decimal places).

Double the number of scores in each treatment by simply repeating the original scores in each treatment a second time. For example, the n = 8 scores in treatment I become 1, 4, 2, 1, 1, 4, 2, 1. Note that this will not change the treatment means, but it will double SSbetween treatmentsbetween treatments, SSbetween subjectsbetween subjects, and the SS value for each treatment. For the new data, use a repeated-measures ANOVA with α =.05 to determine whether there are significant differences among the treatments and compute η² to measure the size of the treatment effect.

Source of Variation	Sum of Squares	ANOVA Table for Doubled Sample	Mean Square	F
Degrees of Freedom
Between treatments
Within treatments
Between subjects
Error
Total

Critical value for the F-ratio =

(to three decimal places).

Reject the null hypothesis. There are significant differences among the three treatments.

Fail to reject the null hypothesis. There are significant differences among the three treatments.

Reject the null hypothesis. There are no significant differences among the three treatments.

Fail to reject the null hypothesis. There are no significant differences among the three treatments.

η² =

(to three decimal places).

Describe how doubling the sample size affected the value of the F-ratio and the value of η².

Doubling the sample size the F-ratio; it η².

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