This suggests a possible interaction effect, based on gender. The plot tells us that the drug reduces anxiety more effectively for women than for men. But is the reduction significant? To answer that question, we need to conduct a statistical test. In this section, we work through two problems to compare regression analysis with and without interaction terms. With each problem, the goal is to examine effects of drug dosage and gender on anxiety levels. In the table, notice that we've expressed gender as a dummy variable , where 1 represents females and 0 represents non-females in this case, males.
Notice also that the variable in the fourth column DG is an interaction term, with a value equal to the product of dose times gender. First, let's ignore the interaction term. When we regress dose and gender against anxiety, we get the following regression table. We see that both dose and gender are statistically significant at the 0. And, with further analysis, we find that the coefficient of multiple determination is a respectable 0.
Now, let's include the interaction term in our analysis. When we regress dose, gender, and the dose-gender interaction against anxiety, we get the following regression table.
We see that the interaction between dose and gender is statistically significant at the 0. In order to find an interaction, you must have a factorial design, in which the two or more independent variables are "crossed" with one another so that there are observations at every combination of levels of the two independent variables.
For example, if you were interested in the effects of practice and stress level on memory task performance, you might decide to employ a factorial design. You manipulate practice by having participants read a list of words either once or five times. You also manipulate stress level by having two conditions: in one low stress , participants are told that the number of words that they recall is unimportant, and in the other high stress , participants are told that most people can recall all words in the list, and that they are expected to be able to do so as well.
Your dependent variable is the number of words recalled from the word list. In this design, you would need to have participants in each of the four cells of the design : low stress and one practice, low stress and five practices, high stress and one practice, and high stress and five practices. Let's say here that you had 25 participants in each of these four cells. Now, if the two factors in the study practice and stress interact, this means that the effect of one factor depends on the level of the other factor.
Let's insert some data to see if there is an interaction in this study. Email Required, but never shown. Featured on Meta. Now live: A fully responsive profile. Related 5. Hot Network Questions. Question feed. Cross Validated works best with JavaScript enabled. Accept all cookies Customize settings. Second, the main effect of repetition seems to be clearly present. The more times people saw the items in the memory test once, twice, or three times , the more they remembered, as measured by increasingly higher proportion correct as a function of number of repetitions.
Yes, there is. Remember, an interaction occurs when the effect of one IV depends on the levels of an another. The delay IV measures the forgetting effect.
Does the size of the forgetting effet change across the levels of the repetition variable? Yes it does. With one repetition the forgetting effect is. With two repetitions, the forgetting effect is a little bit smaller, and with three, the repetition is even smaller still. So, the size of the forgetting effect changes as a function of the levels of the repetition IV. There is evidence in the means for an interaction. You would have to conduct an inferential test on the interaction term to see if these differences were likely or unlikely to be due to sampling error.
If there was no interaction, and say, no main effect of repetition, we would see something like this:. The correct answer is that there is evidence in the means for an interaction. Remember, we are measuring the forgetting effect effect of delay three times.
The forgetting effect is the same for repetition condition 1 and 2, but it is much smaller for repetition condition 3. The size of the forgetting effect depends on the levels of the repetition IV, so here again there is an interaction. Here, there are three IVs with 2 levels each. There are three main effects, three two-way 2x2 interactions, and one 3-way 2x2x2 interaction. We will use the same example as before but add an additional manipualtion of the kind of material that is to be remembered.
For example, we could present words during an encoding phase either visually or spoken auditory over headphones. Now we have two panels one for auditory and one for visual. You can think of the 2x2x2, as two 2x2s, one for auditory and one for visual. We can see that the graphs for auditory and visual are the same. They both show a 2x2 interaction between delay and repetition. People forgot more things across the week when they studied the material once, compared to when they studied the material twice.
There is a main effect of delay, there is a main effect of repetition, there is no main effect of modality, and there is no three-way interaction. What is a three-way interaction anyway? That would occur if there was a difference between the 2x2 interactions. For example, consider the next pattern of results. We are looking at a 3-way interaction between modality, repetition and delay. What is going on here? These results would be very strange, here is an interpetation.
For auditory stimuli, we see that there is a small forgetting effect when people studied things once, but the forgetting effect gets bigger if they studies things twice. A pattern like this would generally be very strange, usually people would do better if they got to review the material twice.
The visual stimuli show a different pattern. We see that there is an interaction between delay the forgetting effect and repetition for the auditory stimuli; BUT, this interaction effect is different from the interaction effect we see for the visual stimuli.
The 2x2 interaction for the auditory stimuli is different from the 2x2 interaction for the visual stimuli. In other words, there is an interaction between the two interactions, as a result there is a three-way interaction, called a 2x2x2 interaction. We will note a general pattern here.
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