Understanding Main Effects and Interactions

Understanding Main Effects and Interactions A main effect is the effect of a single independent variable on a dependent variable – ignoring all other independent variables. For example, imagine a study that investigated the effectiveness of dieting and exercise for weight loss. Study participants were separated into 4 different groups, those that dieted only, exercised only, did both, or did nothing. The chart below indicates the weight loss for each group after two weeks. Week 2 weight loss in pounds as a function of treatment condition Diet Exercise Yes No Yes 20 8 14 No 10 -2 4 15 3 Think to yourself – what are the independent and dependent variables? Let’s assume that all numerical differences greater than 2 in this fictitious dataset are significant (3 = 4; 14 = 15; 8 = 10). We would have 2 main effects: 1) Exercise (M = 14) results in more weight loss than no exercise (M = 4) 2) Dieting (M = 15) results in more weight loss than no dieting (M = 3) Each of these main effects only looks at the marginal data – it disregards that there may be other independent variables. When you assess possible interactions, you assess whether the different conditions for an independent variable (here, yes or no) produce results that differ depending on what condition you consider for a second independent variable. So, exercise is always better than no exercise (20 > 10; 8 > -2) and dieting is always better than no dieting (20 > 8; 10 > -2) (the main effects establish this). But, dieting and exercise is particularly effective than either dieting or exercise alone (20 > 15; 20 > 14). Sometimes you can have no main effects but still have an interaction: Consider a study of memory for show type. Males and females are shown two different television shows (sports or Oprah) and tested for content memory afterwards. The data is as follows: Memory of televised material as a function of gender and show type Television Memory Gender Sports Oprah Male 50 10 30 Female 10 50 30 30 30 Again, consider the independent and dependent variables. Remember, for main effects we only consider one at a time, individually. There are no main effects. Males and females demonstrated equal levels of recall (M = 30). There was just as much recall for sports related shows as there was for Oprah (M = 30). But there is interaction – the second independent variable changes the interpretation of the data. Males do recall more than females if/when the content is sports (50 > 10). And, females do recall more than males if/when the content is Oprah (50 > 10). [Said differently, sports is recalled more when the viewer is male (M = 50) vs. female (M = 10). Oprah is recalled more when the viewer is female (M = 50) vs. male (M = 10).] Sometimes you have main effects but no interactions: Imagine a study that examines the reading and math ability of elementary compared to middle schools students. Reading ability is operationalized as the number of words you can read in 2 minutes and Math as the number of math problems you can complete in 5 minutes. Academic ability in reading and math as a function of grade level School Subject Grade Level Reading Math Elementary 100 20 60 Middle School 200 120 160 150 70 The results show that there are two main effects. Students are better at reading (M = 150) than math (M = 70). And middle school students (M = 160) have higher ability than elementary school students (M = 60). Taking into account both independent variables simultaneously does not change these results. Elementary and middle school students are both better in reading compared to math. (Said differently, reading ability is higher than math ability for both elementary and middle school students.) Be careful. Comparing this to the weight loss example you might erroneously conclude that reading is better than math particularly for middle school students. Note that the differences between reading and math ability for both groups is 80 points (100 – 20 = 80; 200 – 120 = 80). There is no significant difference between these values. Similarly, you might state that middle school students have higher ability than elementary school students particularly in reading. Again, middle school students are 100 points better than elementary school students in reading (200 vs. 100) and 100 points better in math (120 vs. 20). Middle school students are stronger than elementary school students but the degree of their superiority over them is equal in both reading and math. Reading scores are greater than math scores but equally greater for both grade levels.