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Essentials of Statistics for the B...

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

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Section
BuyFindarrow_forward

Essentials of Statistics for the B...

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

The following data are from a two-factor study examining the effects of two treatment conditions on males and females.

a.    Use an ANOVA with α = .05 for all tests to evaluate the significance of the main effects and the interaction.

b. Compute η2 to measure the size of the effect for each main effect and the interaction.

  Factor B: Treatment

  B1 B2 B3  
Male 3 1 10  
  1 4 10  
  1 8 14  
  6 6 7

TROW1 =90

ROWI

  4 6 9  
  M= 3 M = 5 M = 10  
  T = 15 T=25 T= 50  
  SS = 18 SS =28 SS = 26 N = 30
Factor A: 0 2 1 G = 120
Gender 2 7 I ΣX2 = 860
  0 2 1  
  0 2 6 TROW2 = 30
Female 3 2 1  
  M = 1 M = 3 M = 2  
  T =5 T =15 T =10  
  SS =8 SS =20 SS = 20  

TCO4.1 = 20 TCO4.2 = 40 TCO4.3 = 60

a.

To determine
Using an ANOVA with α=0.05 for all tests to evaluate the significance of the main effects and the interaction.

Explanation

Given info:

The following data are given in the question:

 Factor B
    B1 B2 B3  
Factor AMale 3 1 10 Trow1=90
1 4 10
1 8 14
6 6 7
4 6 9
M=3T=15SS=18 M=5T=25SS=28 M=10T=50SS=26 N=30
Female 0 2 1

 

 

G=120X2=860Trow2=30

2 7 1
0 2 1
0 2 6
3 2 1
M=1T=5SS=8 M=3T=15SS=20 M=2T=10SS=20
Total = 20 Total = 40 Total = 60  

Calculation:

Total variability:

Total sum of squareis calculated as:

SStotal=X2G2N=860(120)230=380

Total degree of freedomis calculated as:

dftotal=N1=301=29

Within treatment:

Sum of square within treatment is calculated as:

SSwithintreatments=SSeachtreatments=18+28+26+8+20+20=120

Degree of freedom within treatmentis calculated as:

dfwithintreatments=(4+4+4)+(4+4+4)=24

Between treatment variability:

Sum of square between treatmentsis calculated as:

SSbetweentreatment=SStotalSSwithin=380120=260

Degree of freedom between treatments is calculated as:

dfbetweentreatment=number of cells 1=61=5

For factor A, the row totals are 90 and 30, and each total was obtained by adding nothing

b.

To determine

Compute: The value of η2 to measure the size of effect for each main effect and the interaction.

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