Estimating Main Effects and interactions

INSTRUCTIONS AND TIPS

To estimate the overall A main effect, find the difference between the average score for all the A2 groups and the average score for the A1 groups.
If there is no difference between the A2 groups' average and the A1 groups' average, there is no evidence of an A main effect.
If, on the other hand, the average score for the A2 groups was 4 and the average score for the A1 groups was 0, you would estimate the overall main effect of A to be 4 (because 4-0 = 4).

Similarly, to estimate the overall B main effect, find the difference between the average score for all the B2 groups and the average score for all the B1 groups.
If there is no difference between the B2 groups' average and the B1 groups' average, there is no evidence of an B main effect.
If, on the other hand, the average score for the B2 groups was 3 and the average score for B1 groups was 1, you would estimate the overall main effect of B to be 2 (because 3-1 = 2).

If you have an interaction, the average effect of your factors does not hold for all your groups.
Therefore, one way to determine whether there is an interaction effect, is to see whether the overall average main effect of A is the same as each of A's simple main effects.
For example, suppose that, on average, the A2 groups score 4 points higher than the A1 groups. Thus, our estimate of the A main effect would be 4.
To see whether there is an interaction, we would see if this 4 point difference between A2 and A1 groups holds when we look at just the B1 groups (i.e., do we see a 4-point difference between the A2-B1 group and the A1-B1 group?). If so, there is no evidence of an interaction.
If, on the other hand, in the B1 conditions, the A2 group scores 8 points LOWER than the A1 group (compared to the A2 groups, on average, scoring 4 points HIGHER than the A1 groups), we would suspect an interaction.
Note you could see whether there is an interaction by determining whether the overall main effect of B is the same as each of B's simple main effects. So, if the B main effect was 3 and both of B's simple main effects were also 3, there would be no evidence of an interaction.
For this exercise, estimate the interaction effect by taking the difference between a factor's average effect and its effect at a specific level of the other factor. To see what you would do, suppose you had the following table

	A1	A2
B1	0	2
B2	1	3

For this table,
the average effect of A is 2. That is, on average, the A2 groups score 2 points higher than the A1 groups.
The average effect of B is 1. That is, on average, the B2 groups score 1 point higher than the B1 groups.
There is no interaction because the average difference between the A1 and A2 groups is 2, and this 2-point difference is mirrored in both the B1 rows as well as in the B2 rows. That is, both of A's simple main effects are the same as A's overall main effect.
Looking at it another way, the average difference between B2 and B1 of 1 is the same as the difference between B2 and B1 in both the A1 columns and the A2 columns. That is, all the B simple main effects are the same as the B overall main effect.
But what if we had the data tabled below?

	A1	A2
B1	1	1
B2	0	4

Once again, the average effect for A is 2 and the average effect of B is 1.
However, in the first row, the B1 row, we do not see a difference of 2 between the A1 and A2 group means. Instead, we see no (0) difference. Because the average effect of A is 2 but the effect of A in this row is 0, you could say the interaction effect was 2 (2-0).
Similarly, in the second row, the B2 row, we do not see a difference of 2 between the A1 and A2 means -- even though the average difference between A1 and A2 is 2. Instead, we see a difference of 4--which is 2 points different than the average difference.
Looking at the columns, we see that, although the average effect of B is 1, the B effect in the A1 column is -1 (2 points off from B's average effect), whereas the B effect in the A2 column is 3 (again, 2 points off from B's average effect).
Because all the simple main effects differ by 2 points from their overall main effects, you could estimate that the interaction effect was about 2 points.

YOUR TURN

Play the game below until you have successfully and confidently identified examples of both main effects and interactions.

	A1	A2
B1
B2

What is your estimate of the A main effect? Enter your answer below.

What is your estimate of the B main effect? Enter your answer below.

What is your best guess about the size of the interaction effect? (You can estimate the interaction effect by figuring out the average difference between a factor's average effect and its effect at a certain level of the other factor.)
Enter your answer below.