### Brief Summary of Chapter 12

In Chapter 11, we extended the logic of the experiment that has two levels of one independent variable to experiments that have more that two levels of one independent variable, as in the example below:
 Level of Caffeine 0 mg 25 mg 50 mg 75mg 100 mg

That study would not be a factorial study because only one factor is being manipulated. Because only one factor is being manipulated, it cannot be used to make conclusions about

1. more than one independent variable
2. interactions between two variable (the effects of combining variables)

In Chapter 12, we extend the logic of the experiment that uses one independent variable to experiments that use two or more independent variables. The main advantages of studying more than two independent variables at a time are

1. If you want to study more than one independent variable, it's more efficient to do one study than to do two.
2. You learn about interactions between independent variables. That is, you can learn whether certain combinations of variables have effects that are different from what would be expected if you knew only each variable's individual effect.

To illustrate, consider the 2 X 2 factorial experiment described in the table below:

No Caffeine Caffeine Group 1 Group 2 Group 3 Group 4
From that study, we could find out
1. the individual effects of two variables (caffeine and noise). By comparing the caffeine groups to the no-caffeine groups, we could find the caffeine effect; by comparing the noise groups to the no-noise groups, we could find the effect of noise.
2. the interaction effect (whether combining the factors led to effects that are different from just adding their individual effects). For example, if caffeine had more of an effect on the noise groups than on the no-noise groups, we would have an interaction. With such an interaction, you really can't talk about caffeine's effect without stating that caffeine's effect is different for the no-noise groups than it is for the noise groups. Put another way, the effect of noise is different for the groups that receive no caffeine than it is for the groups that receive caffeine. So, with an interaction, you can't talk about noise effects without mentioning that the noise effect depends on how much caffeine was administered. .

If, on the other hand, there is no interaction, then you can talk about the effects of noise and caffeine separately. You do not have to qualify your statements about the effects of noise by saying things like "However, the effect of noise is qualified by a noise by caffeine interaction. The effect of noise is different in the no caffeine condition than in the caffeine condition."

To appreciate the difference between main effects and interactions, consider the hypothetical data from the experiment below:

Experiment A
No Caffeine Caffeine 2 4 5 7

In this experiment, noise has an effect: The noise groups score 3 points higher, on average, than the no-noise groups. Caffeine also has an effect: The caffeine groups score, on average,  2 points higher than the no-caffeine groups. However, there is no interaction because the combination of caffeine and noise produces the same effect as we would expect from their individual effects. For example, knowing that the caffeine effect is, on the average 2, how would you complete the table below?  (Don't look at the Experiment A table until you are finished.)

No Caffeine 2 5

Similarly, knowing that the noise effect is 3, on the average, how would you complete the table below?  (don't look at the other tables until you are finished.)

No Caffeine Caffeine 2 4

So, for Experiment A, the average effects of your variables tells the whole story.
Contrast that with Experiment B, where, as before, the average effect of caffeine is 2 and the average effect of noise is 3, but, this time, there is an interaction.

No Caffeine Caffeine 2 3 4 7

Because there is an interaction in Experiment B, the average effects don't tell the whole story. As you can see, caffeine has more of an effect in the noise groups (7-4 =3) than it does for the no-noise groups (3-2 =1). So, if you tried to predict caffeine's effects knowing only its average effect, you would make mistakes. For example, you would probably fill in this table as you did before

No Caffeine 2 4

like so:

No Caffeine Caffeine 2 4 4 6

which is not correct.

To get a general idea of what interactions represent, see Table 12-1 and 12-2 (pp. 475-477).

After explaining interactions, we made two important distinctions.

First, we distinguished between ordinal and disordinal (cross-over) interactions. We pointed out that you can easily tell which type of interaction you have by graphing it. More importantly, we showed how ordinal interactions--rather than meaning that the combination of two variables has a smaller (or bigger) psychological effect than would be expected by looking at the variables' individual effects--could be due to having  ordinal scale data (your scores not accurately describing how much more of a quantity participants had). Cross-over interactions, on the other hand, can't be due to  having  ordinal scale data. Thus, we can usually be more confident of that a cross-over interaction indicates that combining your factors has an effect that is different from the sum of their individual effects. .

Second, we distinguished between "true " ( "strong") independent variables that we can randomly assign (e.g., level of caffeine) and "weak " independent variables that we can't randomly assign (e.g., participant variables, such as gender, personality type, etc.) . We stressed that you can't make causal statements about "weak " independent variables (variables that we do not manipulate).

Finally, you learned that you can add a second variable to a simple experiment to make it a 2 X 2 design. For example, to see whether the main effect of the variable studied in the simple experiment

• was limited to just one stimulus set, you might add the replication factor of stimulus sets.
• depending on a the level of a second variable, you might do a moderating factor study.
If you add a participant variable to a simple experiment, you can't make cause-effect statements about that second variable. However, adding that second variable can improve the simple experiment by
• making your study more powerful(if your second variable was a "blocking variable" that soaked up error variance),
• making better generalizations from your study (e.g., if you included gender as a factorr, you could see whether your experimental factor interacted with gender)