Interaction Effect Show
An interaction effect is the simultaneous effect of two or more independent variables on at least one dependent variable in which their joint effect is significantly greater (or significantly less) than the sum of the parts. The presence of interaction effects in any kind of survey research is important because it tells researchers how two or more independent variables work together to impact the dependent variable. Including an interaction term effect in an analytic model provides the researcher with a better representation and understanding of the relationship between the dependent and independent variables. Further, it helps explain more of the variability in the dependent variable. An omitted interaction effect from a model where a nonnegligible interaction does in fact exist may result in a misrepresentation ... locked icon Sign in to access this contentSign in Get a 30 day FREE TRIAL
sign up today! Lecture 12 Our initial discussion of Analysis of Variance concerned the comparison of two or more groups. Those groups can be considered different "levels" of one independent variable. If we are comparing women to men, there are two levels of gender represented. If the study is an experiment that compares a drug's effect to a control group with no drug, there is one independent variable with two levels: drug and no drug. If we add a third comparison group, say a placebo, we still have one independent variable. We just have three different representations of the independent variable. The drug, no drug, and the placebo are considered different "levels" of the independent variable. A factorial design (and hence, a factorial analysis) introduces another independent variable to be studied simultaneously with the first independent variable, and each independent variable can have two or more levels. Each of the independent variables are now called factors. Example The cells below represent rough approximations of the mean scores on the memory test in the two groups. Study 1
Let's say we wanted to turn this study into a practical public program of some sort that attempts to improve eyewitness memory for details. Because we could not possibly train everyone who might be a potential witness to a crime, we might pick out certain people who are more likely to witness a crime (e.g., convenience store owners, police officers). Because police officers are always witnessing crimes and arrests, and they often have to testify about the incident, we might try to improve their memory for criminal events. We could develop a training course that attempted to improve the memory of police officers for crime details by informing them about various potential fallacies of eyewitness accounts. We then might conduct a second study that evaluates the effectiveness of the training. In that study, we randomly assign police officers to a training condition or to a condition in which they receive no training. At the end of the training period, the police officers are shown a film of a crime and given a memory performance test. If the training was effective, they should have better memory of the incident. Study 2
Instead of conducting two separate experiments, we could combine them both. This would be beneficial for several reasons. First, it would be more economical; it is cheaper and easier to run one experiment instead of two. Second, we could look for any combined effects of the two independent variables. For instance, it might be that the training program would be effective for improving memory, but that the benefits of the training do not extend to violent incidents. When a violent incident occurs, trained police officers are just as likely to miss the details, because the emotional event interferes with memory storage for them also. In other words, although memory is generally improved by the training, the circumstances under which it is effective are limited. If this was the case, we would have the following outcome of our combined study.
In this hypothetical outcome, the training has an effect when there is not a violent incident. However, if there is violence in the film clip, training makes no difference in memory performance. In this sense, the effect on one independent variable (training) depends on the level of the other independent variable (violence). This is an example of an interaction. Interactions imply that the two independent variables combine to have a different effect on the dependent variable. Mathematically, their effects are multiplicative rather than additive. Take the following hypothetical outcome as an example.
Here, there is a difference between the Training and No Training conditions in their effects, but the effect of training is essentially the same in both the Violence and No Violence condition. Training improves memory performance in all groups equally. This is an example of an additive effect, not a multiplicative effect. If the effect is simply additive, there is no interaction effect. Main Effects
In this example, there is a main effect for the training variable, because, overall, training improves memory. To see the main effect for memory, we have to average over the two Violence/No Violence cells. We do that separately for the Training and No Training condictions. What we wind up with is two marginal means: 4.3 overall for the No Training conditions and 7.3 overall for the Training condition. Because 7.3 is larger than 4.3, there seems to be a difference the Training and No Training conditions (of course, we would have to test this for signficance). The difference between these marginal means represents a main effect. To look at the main effect for the Violence independent variable, we would compare the Violence and No Violence combining all the participants in the No Training and Training conditions. Overall, the Violence conditions had poorer memory than the No Violence condition (4.0 vs. 7.6). So, in general, there seems to be two main effects in this study, and, because the effects are additive, there is no interaction between the two independent variables. Their effects on the dependent variable are separate or independent. Main effects and interactions do not depend on one another. That is, there can be one or two main effects, and an interaction can occur in combination with either main effect, both main effects, or no main effects. An easy way to tell if there is an interaction is to plot the four cell means on a graph. This can be done with a line graph or a histogram, although I believe the line graph offers a simpler interpretation. If the two lines are parallel, there is no interaction. If they are not parallel, there is an interaction. Click here for some examples of possible outcomes of main effects with no interactions. Click here for some graphs that present examples of interactions. Naturally, for any of these examples, we do not really know if there is an interaction or a main effect until we test for them. There will be more on that below, but first I need to make one more distinction. Simple Effects
Any combination of simple effects may occur when there is an interaction. When a significant interaction is found, simple effects are usually tested to discover where the differences lie. With larger designs with more cells, this is even more critical. One could do t-tests to compare means, but this is problematic because of alpha inflation. Testing Simple Effects Factorial ANOVA
Planned Contrasts From a statisticians point of view (and yours too), planned contrasts are better than separate t-tests. The biggest difference is that the power is greater for a planned contrast. If you think about it, the use of a larger d.f. and a larger sample size to estimate the standard error should lead to greater power. Planned contrasts can also be formulated to test for a certain interaction pattern (e.g., a cross-over X pattern), and these are referred to as interaction contrasts. Interaction contrasts are not used very often, but they are certainly legitimate. They are also more powerful than the omnibus factorial ANOVA, because they require a particular pattern of results to be predicted. More Complex Factorial Designs Within-Subjects and Mixed Designs The computations and details of the within-subjects factorial are a bit more complex, so we will not be able to cover them in this class. If you ever need to analyze a study with these complex features, there are a couple of excellent references on ANOVA that might be consulted: Keppel, G. (1991). Design and analysis: A researcher's handbook. Englewood Cliffs, NJ: Prentice Hall. Winer, B.J. Brown, D.R., Michels, K.M. (1991). Statistical principles in experimental design. New York : McGraw-Hill. Can you have a main effect and an interaction?There will always be the possibility of two main effects and one interaction. You will always be able to compare the means for each main effect and interaction. If the two means from one variable are different, then there is a main effect.
Is it possible to have a significant interaction when both main effects are significant?There is really only one situation possible in which an interaction is significant and meaningful, but the main effects are not: a cross-over interaction. The two grey dots indicate the main effect means for Factor A. Their height is pretty much the same, so there would be no main effect for Factor A.
Do you report main effects or interactions first?You should report both the main effects and the Interaction. Once there is a significant interaction then the main effects could be hidden or distorted due to the interaction with the second independent variable.
Why is it important to study interactions rather than just main effects quizlet?According to the textbook, why is it important to study interactions? Many outcomes in psychology are interactions. They are easier to understand than main effects. They are more complicated than other analyses.
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