Question

Mini Practice Problem #11

For the data in the following matrix:

	No Treatment	Treatment	Overall Mean
Male	10	20	15
Female	14	16	15
Overall Mean	12	18

If you were to perform a factorial ANOVA, how would you answer the following questions.

What numbers are compared to evaluate the main effect for the treatment? If there was a significant treatment main effect, how would you interpret this finding?

What numbers are compared to evaluate the main effect for gender? If there was a significant gender main effect, how would you interpret this finding?

If there was a treatment x gender interaction effect, what numbers or further statistical analyses would you conduct to determine where differences existed?

Answer 1

1.

12 and 18 are compared to evaluate the main effect for the treatment.

Interpretation:

The main effect of treatment on dependent variable was significant such that the participants who received treatment had higher scores than who did not receive the treatment (because treatment mean:18 > No treatment mean:12).

2.

15 and 15 are compared to evaluate the main effect for gender.

Interpretation:

The main effect of gender on dependent variable was significant such that the gender with higher mean had higher scores than the gender with lower mean (however, here two means are equal, 15 and 15 and so, no significant effect).

3.

If there was a treatment x gender interaction effect, plot the interaction and describe the nature of the interaction(which should be evident from the plot) and test simple effects.

Interactions are about differences among differences. None of the individual differences needs to be significant for a significant interaction.

For 2x2 designs we should never perform a post hoc test on the interaction because the interaction itself tells us all of the necessary information that the effect of treatment on the dependent variable changes with another independent variable being gender.

The rationale for testing simple effects is to know at what levels of a second variable, the variable in question has a significant effect. Testing simple effects is done following an interaction but not to help understand the interaction. It is done to see where the effect of the variable is significantly different from zero.