Interactive Exercise #2 ANOVA with a small dataset

a. Means

Mean for Group 1( ) = (2 + 6) / 2 = 4

Mean for Group 2 ( ) = (5 + 7) / 2 = 6

Grand Mean for Y ( ) = (2 + 6 + 5 + 7) / 4 = 5

b. SS Total Calculations

Case

  X

   Y

  1

1

2

2-5 = -3

(-3)2 = 9

  2

1

6

6-5 = 1

(1)2 = 1

  3

2

5

5-5 = 0

(0)2 = 0

  4

2

7

7-5 = 2

(2)2 = 4

 

 

 

 

Σ = 14

d. See b above. Both values should be 14

 f. SS Between Groups Calculations

Case

X

Y

 

  1

1

2

4

4-5 = -1

(-1)2 = 1

  2

1

6

4

4-5 = -1

(-1)2 = 1

  3

2

5

6

6-5 = 1

(1)2 = 1

  4

2

7

6

6-5 = 1

(1)2 = 1

 

 

 

 

 

Σ = 4

g. See f above for SS. Should correspond to SS Regression.

h. Regression line intersects X = 1 at Y = 4.

Which Y' values from Exercise #1 does this correspond to?  Y' = 4 for X = 1

Regression line intersects X = 2 at Y = 6.

Which Y' values from Exercise #1 does this correspond to?  Y' = 6 for X = 1

 

i. SS Within Groups Calculations

Case

X

Y

(Group Mean)

  1

1

2

4

2-4 = -2

(-2)2 = 4

  2

1

6

4

6-4 =  2

(2)2 = 4

  3

2

5

6

5-6 = -1

(-1)2 = 1

  4

2

7

6

7-6 =  1

(1)2 = 1

 

 

 

 

 

Σ = 10

k. See i for SS.  Corresponds to SS Error.

l.  Calculation of F

F = [4 / 1] / [10 / 2]  =   4 / 5 = 0.8. 

n. Calculation of Eta-Squared

4 / 14 =   .286. Corresponds to r2.

Back to Module 4 Exercise 2