You decide to conduct a factorial experiment to test the effectiveness of one environmental factor and one physiological factor on a physical health outcome. As the environmental factor, you choose two levels of oral hygiene. As the physiological factor, you choose three levels of cortisol value. The outcome is the number of cavities, and the research participants are kindergartners. You conduct a two-factor ANOVA on the data. The two-factor ANOVA involves several hypothesis tests. Which of the following are null hypotheses that you could use this ANOVA to test?
a. Cortisol value has no effect on the number of cavities.
b. The effect of oral hygiene on the number of cavities is no different from the effect of cortisol value.
c. oral hygiene has no effect on the number of cavities.
d. There is no interaction between oral hygiene and cortisol value.
The results of your study are summarized by the corresponding sample means below. Each cell reports the average number of cavities for 6 kindergartners.
Factor B:= Cortisol Value A:= oral hygine
B
Low Medium High
A Low M=3.00,T=18,SS=0 M=3.17,T=19,SS=0.8333 M=4.17,T=25,SS=0.8333 T_{row1}=62
High M=3.33,T=20,SS=1.3333 M=3.50,T=21,SS=1.5000 M=3.83,T=23,SS=0.8333 T_{ROW2}=64
T_{COL1}=38 T_{COL2}=40 T_{COL3}=48
You perform an ANOVA to test that there are no main effects of factor A, no main effects of factor B, and no interaction between factors A and B, some of the results are presented in the following ANOVA table.
ANOVA:
Source SS df MS F
Between-treatments 5.667 5
FactorA 0.1111 0.62
FactorB 2.3334 13.12
AXB-interaction 0.8890
Within-treatments
Total 11.0000 35
At a significance level
α
=
.05
, the main effect due to fac A is , the main effect due to factor B is , and the interaction effect between the two factors is
(Choices for each of the 3 blanks : significant or not significant)