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Suppose people engaged in a boring task and were then asked to recruit other participants, for which they would be paid either $1 or $20. How enjoyable would the people in each group say they found the boring task, where a rating of 1 reflected low enjoyment and a rating of 7 reflected high enjoyment?
Students in several classes tried to estimate the ratings that real participants in such research would give. Some students were familiar with research like this, which involves cognitive dissonance, and some were not. The students who knew about the research were considered Not Naive; students who did not know about the research were considered Naive. Their ratings appear below.
Ratings as a function of Naivete and Reward:
Naive: Mean = 3.91  $1 Reward: Mean = 4.10 
Not Naive: Mean = 4.27  $20 Reward: Mean = 4.22 
Does it look like there is a difference in ratings between the Naive and the Not Naive students? Does it look like there is a difference as a function of the size of the reward? Think about it for a moment. When you come to a conclusion, you can see the results of the statistical analysis for these main effects.
Mean ratings broken down by variable and condition:
Reward 

Naivete  $1 
$20 

Naive  3.30 
4.53 
3.91 
Not Naive  4.44 
4.09 
4.27 
4.10 
4.22 
Does there seem to be a different pattern of results for the Naive and Not Naive people, depending on whether they are in the $1 or the $20 condition? That is, do Naive students show the same type of difference between the $1 and the $20 conditions as the Not Naive students do? Think about it for a moment. when you come to a conclusion, you can see the results of the statistical analysis for this interaction.
Sometimes main effects, whether they are significant or not, are not all that informative if there is a significant interaction. Why might the interaction be more helpful than main effects in understanding the behavior you are investigating?
Graphing the Results
Sometimes it is useful to get a picture of the results. The bar graph below shows the pattern of data for the study. How would you explain these results in words to a person who didn't know statistics and psychology?
Results of the ANOVA for the main effect of the Naivete independent variable: F(1,177) = 1.333, p = .250
Results of the ANOVA for the main effect of the Reward independent variable: F(1,177) = 2.131, p = .146
When you have a factorial design, you consider a main effect for each independent variable. The analysis of the main effects involves considering a single independent variable, ignoring any other IVs. Thus, for an analysis of the main effects in this case, we are looking at a simple twogroup comparison for each main effect because each IV in this study had two groups.
One comparison involves the main effect of Naivete, assessing whether the Naive group and the Not Naive group differ in their ratings of enjoyment. The second main effect involves whether participants gave different ratings depending on whether they would expect $1 or $20 for engaging in the task. With respect to main effects, when you consider Naivete, you ignore Reward entirely; when you consider Reward, you ignore Naivete entirely.
Go back to the information on main effects
The results of the ANOVA for the interaction between Naivete and Reward: F(1,177) = 6.825, p = .010
This interaction effect is significant. How can you tell from the information given?
When you assess possible interactions, you assess whether the different conditions for an IV produce results that differ depending on the what condition you consider for a second IV. If you can't make a simple statement that one level of an IV always produces a predictable effect, regardless of the level of a second IV, you have an interaction between the variables.
Go back to the information on the interaction
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Created on March 17, 2004