The following table summarizes the results of a twofactor AN

The following table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment with two levels of factor A, three levels of factor B, and n = 8 participants in each treatment condition. Again, use the lecture notes as your guide for this.

          a. Fill in ALL missing values in the table that have a question mark.

b. Calculate F for each main effect and for the interaction. State if there is a significant main effect for either factor A or factor B, and if there is a significant interaction. Use an alpha of .01.

c. Compute ?² (the percentage of variance accounted for) for each of the main effects and for the interaction. .

Source

SS

Df

MS

F

Between tx

124

5?

24.8?

Factor A

40

1?

40?

F_A=10?

Factor B

64?

2?

32

F_B=8?

A x B

20?

2?

10?

F_axb =2.5?

Within Tx

168?

42?

4?

Total

292

47?

State the F value for each effect (Factor A, B and AxB), state the critical value of F for each test, and state whether F is significant, and whether you can or cant reject the null hypothesis.

2 points Factor A -.

2 points Factor B

2 point Interaction AxB

Calculate the variance explained by factors A, B and Ax B, separately.

          1 point Factor A

         

          1 point Factor B

         

          1 point Interaction AxB -

Source	SS	Df	MS	F
Between tx	124	5?	24.8?
Factor A	40	1?	40?	FA=10?
Factor B	64?	2?	32	FB=8?
A x B	20?	2?	10?	Faxb =2.5?
Within Tx	168?	42?	4?
Total	292	47?

Solution

a. The ANOVA table is

Source

SS

Df

MS

F

Between tx

124

5

24.8

Factor A

40

1

40

F_A=10

Factor B

64

2

32

F_B=8

A x B

20

2

10

F_axb =2.5

Within Tx

168

42

4

Total

292

47

b. F value and critical value for each effect (Factor A, B and AxB)

Source	SS	Df	MS	F
Between tx	124	5	24.8
Factor A	40	1	40	FA=10
Factor B	64	2	32	FB=8
A x B	20	2	10	Faxb =2.5
Within Tx	168	42	4
Total	292	47