Question

A researcher computes the following 2 x 3 between-subjects ANOVA, in which 11 participants were observed in each group. Which effect was significant at a 0.05 level of significance using the two-way between-subjects ANOVA?

Source of Variation SS df MS F
Factor A 10
Factor B
A × B 40
Error 240
Total 340
A. one of the main effects only
B. Factor A and the A x B interaction
C. Factor B and the A × B interaction
D. There were no significant effects.

Answer 1

D. There were no significant effects.

Explanation:

The table below shows the representation of the significance level using the two-way between subjects ANOVA.

Source of Variation SS df MS F P-value

Factor A 10 1 10 0.21 0.660

Factor B 50 2 25 0.52 0.6235

A × B 40 2 20 0.42 0.6783

Error 240 5 48 - -

Total 340 10 - - -

From the table above , the SS(B) is determined as follows:

SS(B) = SS(Total)-SS(Error-(A×B)-A)

= 340-(240-40-10)

= 50

A researcher computes the following 2 x 3 between-subjects ANOVA;

k=2

n=3

N(total) = no of participants observed in each group =11

df for Factor A= (k-1)

=(2-1)

=1

df for Factor B = (n-1)

=(3-1)

=2

df for A × B

= 2 × 1

= 2

df factor for total

=(N-1)

=11-1

=10

MS = SS/df

Thus, from the table, the P-Value for all data is greater than 0.05, therefore we fail to reject H₀.