   Chapter 13, Problem 26P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Research indicates that paying students to improve their grades simply does not work (Fryer, 2011). However, paying students for specific tasks such as reading books, attending class, or doing homework does have a significant effect. Apparently, students on their own do not understand how to get good grades. If they are told exactly what to do, however, the incentives work. The following data represent a two-factor study attempting to replicate this result.   Paid for Homework Not Paid for Homework Paid for Grades 14 2 7 7 10 5 9 7 11 3 9 6 Not Paid for Grades 13 7 7 2 9 4 7 2 11 6 7 3 a. Use a two-factor ANOVA with α = .05 to evaluate the significance of the main effects and the interaction. b. Calculate the η2 values to measure the effect size for the two main effects and the interaction. c. Describe the pattern of results. (How does paying for grades influence performance? How does paying for homework influence performance? Does the effect of paying for homework depend on whether you also pay for grades?)

a.

To determine

To Find: Using 2 factor ANOVA with α=0.05 to evaluate the significance of main effects and the interaction.

Explanation

Given info:

The data given as:

 Category Paid for Homework Not paid for homework Paid for Grades 14 2 7 7 10 5 9 7 11 3 9 6 Not paid for Grades 13 7 7 2 9 4 7 2 11 6 7 3

Calculation:

With the given data can easily calculate T, M and SS for all of the treatments. For paid for homework and paid for grades values are:

T=60M=10SS=28

For paid for homework and not paid for grades values are:

T=54M=5SS=32

For not paid for homework and paid for grades values are:

T=30M=5SS=22

For not paid for homework and not paid for grades values are:

T=24M=9SS=22

Also,

N=24,G=168,X2=1436

For a two factor study, there are 3 separate hypotheses, the two main effects and the interaction.

For Factor A, the null hypothesis states that there is no difference.

For factor B, the null hypothesis states that there is no difference in performance among the 2 treatment conditions.

μ0:μB1=μB2

For A×B interaction, the null hypothesis states that the effect of either factor does not depend on the levels of other factor.

Here,  use α=0.05 for tests

Sum of square total is calculated as:

SStotal=X2G2N=1436168224=260

Sum of square within treatment is calculated as:

SSwithintreatment=SSeachtreatment=28+22+32+22=104

Now sum of square between treatments is calculated as:

SSbetweentreatment=T2nG2N=60206+30206+54206+24206(168)224=156

The corresponding degree of freedom is:

dftotal=N1=241=23

Now the degree of freedom within treatment is calculated as:

dfwithintreatment=dfeachtreatment=5+5+5+5=20

Similarly, the degree of freedom between treatments is calculated as:

dfbetweentreatment=number of cells1=41=3

The MS within treatment is calculated as:

MSwithintreatment=10420=5

b.

To determine

To Calculate: The η2 values to measure the effect size for the 2 main effects and the interaction.

c.

To determine

To Describe: The pattern of results.

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