Main Effect and Interaction Effect in Analysis of Variance

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  • 0:04 Dependent &…
  • 1:11 Main Effects
  • 3:16 Interaction Effects
  • 3:54 Results of a Two-Way ANOVA
  • 4:31 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Analysis of Variance (ANOVA) is a statistical test used to identify the effects of independent variables on the outcome of an experiment. In this lesson, learn about main effects and interaction effects and how ANOVA can be used to test for both.

Dependent & Independent Variables

Jamal works for a company that has developed a new drug to treat a certain type of cancer. It's Jamal's job to design a study that will determine which doses of the drug are most effective and if the effectiveness depends on the initial size of the tumor. How can he do this?

In Jamal's study, there are two independent variables: original tumor size and drug dosage. These are called independent variables because they are the things that he can control and change.

He would need to divide the patients into groups based on both tumor size and drug dosage. If there are three different tumor sizes and four different drug doses being tested, there will be 12 different groups of patients.

number of groups (N) = 3 x 4 = 12

The next thing to consider is what to measure at the end of the study. This is known as the dependent variable, and in this case, Jamal would probably want to measure the size of each patient's tumor at the end of the study. Then he could calculate the percentage of the original tumor that remains after treatment. This percentage would be the dependent variable, and Jamal could use it to determine if there are any differences that are due to either of the independent variables or to an interaction between them.

Main Effects

To determine if drug dosage or original tumor size affect the final tumor size, Jamal needs to test for three different effects:

Effect #1: Drug dosage - Are there any differences in the final tumor size that can be attributed to the drug dosage?

Effect #2: Original tumor size - Are there any differences in the final tumor size that can be attributed to the original tumor size?

Effect #3: Interaction between drug dosage and original tumor size - Is there an interaction between drug dosage and the original tumor size in determining the final tumor size?

Effects #1 and #2 are known as main effects because they are exclusively due to one factor or the other. In statistics, a main effect is the effect of just one of the independent variables on the dependent variable. The first step in determining if the main effect results in statistically significant differences in the dependent variable is calculating the marginal mean of each group. To find the marginal mean, average the means of the individual groups. For example, in the table below, the marginal mean for the 250 mg/kg treatment group is found by adding all the means in that column (88%, 92%, and 105%) and dividing by three to get 95%.

main and interaction effects table

The main effect for each factor is determined by comparing marginal means. For example, to see if there are differences due to the drug concentration, Jamal should compare the marginal means for each concentration (95%, 86%, 61%, 53%).

Just calculating the marginal means, however, isn't enough to determine if the different concentrations of drug result in statistically significant differences in tumor reduction. To do that, Jamal would have to take this data and perform an analysis of variance, commonly known as ANOVA. ANOVA is a statistical test that's used to determine if there are differences between groups when there are more than two treatment groups. There are different types of ANOVA that should be used depending on the situation, but in this case, Jamal should use a two-way ANOVA because he's testing the effects of two independent variables on the dependent variable.

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