Quantitative Methods

Quantitative Methods
The results from a two-factor experiment can be presented in a matrix with the levels of one factor forming the rows and the levels of the second factor forming the columns, with a separate sample in each of the matrix cells. Using this matrix structure, describe what is meant by the “main effect” for each factor and the “interaction” between factors.
The following data were obtained from a two factor independent-measures experiment with n=5 participants in each treatment condition.

B1
B2
B3

A1
M = 3
SS = 18
M = 6
SS = 28
M= 9
SS = 26

A2
M = 1
SS = 8
M = 4
SS = 20
M = 1
SS = 20
a. State the hypotheses for each of the three separate tests included in the two-way ANOVA.
b. Calculate degrees of freedom and locate the critical region for each of the three tests.
c. Calculate the three F-ratios.
d. State a conclusion for each test.

3. The following table Summarizes the results from a two-factor study with three levels of factor A and 3 levels of factor B using a separate sample of n = 9 participants in each treatment condition. Fill in the missing values (Hint: start with the df values).

Source
df
SS
MS
F
Between groups

144
A

18

B

A x B

7.0
Within (error)

Total

360

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