The following data are from a twofactor 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 η^{2} to measure the size of the effect for each main effect and the interaction.
Factor B: Treatment
B_{1}  B_{2}  B_{3}  
Male  3  1  10  
1  4  10  
1  8  14  
6  6  7  T_{ROW1} =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  ΣX^{2} = 860 
0  2  1  
0  2  6  T_{ROW2} = 30  
Female  3  2  1  
M = 1  M = 3  M = 2  
T =5  T =15  T =10  
SS =8  SS =20  SS = 20 
T_{CO4.1} = 20 T_{CO4.2} = 40 T_{CO4.3} = 60
a.
Given info:
The following data are given in the question:
Factor B  




Factor A  Male  3  1  10 

1  4  10  
1  8  14  
6  6  7  
4  6  9  



 
Female  0  2  1 


2  7  1  
0  2  1  
0  2  6  
3  2  1  




Total = 20  Total = 40  Total = 60 
Calculation:
Total variability:
Total sum of squareis calculated as:
Total degree of freedomis calculated as:
Within treatment:
Sum of square within treatment is calculated as:
Degree of freedom within treatmentis calculated as:
Between treatment variability:
Sum of square between treatmentsis calculated as:
Degree of freedom between treatments is calculated as:
For factor A, the row totals are 90 and 30, and each total was obtained by adding nothing
b.
Compute: The value of
Understanding Basic Statistics
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus: Early Transcendentals
Trigonometry (MindTap Course List)
Elementary Geometry For College Students, 7e
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: Early Transcendentals
Calculus of a Single Variable
Precalculus: Mathematics for Calculus (Standalone Book)
Finite Mathematics for the Managerial, Life, and Social Sciences
Contemporary Mathematics for Business & Consumers
Elementary Technical Mathematics
Mathematical Excursions (MindTap Course List)
Finite Mathematics
Elements Of Modern Algebra
Multivariable Calculus
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Finite Mathematics and Applied Calculus (MindTap Course List)
Applied Calculus
Calculus (MindTap Course List)
Calculus: Early Transcendental Functions (MindTap Course List)
Single Variable Calculus
Mathematical Applications for the Management, Life, and Social Sciences
Intermediate Algebra
Calculus: An Applied Approach (MindTap Course List)
Calculus: Early Transcendental Functions
Introduction To Statistics And Data Analysis
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Multivariable Calculus, 8th
Elementary Geometry for College Students