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Essentials of Statistics for the B...

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

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BuyFindarrow_forward

Essentials of Statistics for the B...

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

The following table summarizes the results from a two-factor study with 2 levels of factor A and 3 levels of factor B using a separate sample of n = 11 participants in each treatment condition. Fill in the missing values. (Hint: Start with the df values.)

Source SS df MS  
Between treatments _____ ____    
Factor A _____ _____ _____ F = 7
Factor B _____ _____ _____ F =8
A × B Interaction _____ _____ _____ F = 3
Within treatments 240 _____ _____  
Total ____ ____    

To determine
The missing values in the ANOVA table.

Explanation

Given info:

The design is in two-factor study with 2 levels of factor A and 3 levels of factor B and the sample size is n=11.

Calculation:

Let r, c and k represent the numbers of levels of factor A, numbers of levels of factor B and total numbers of treatment conditions respectively.

r=2c=3k=3×2=6

Let n and N represents the numbers of participants in each treatment and total numbers of participants in study. Then,

n=11N=k×n=6×11=66

Calculating the dftotal is:

For total:

dftotal=N1=661=65

For between treatments:

dfbetweentreatments=k1=61=5

For within treatments:

dfwithintreatments=k×(n1)=6×(111)=6×10=60

For factor A:

dfA=r1=21=1

For factor B:

dfB=c1=31=2

For interaction effect:

dfA×B=dfbetweentreatmentsdfAdfB=512=2

Calculating the mean sum of squares:

For within treatments:

MSwithintreatments=SSwithintre

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