Two Analysis of Variance

Two-way Analysis of Variance

Why is this Important?

Big hint - If you haven't read our Oneway Workshop - do that first!

How do you determine what factors are significant when you have two independent variables?

Two F -ratios, one for each factor will tell us this!

Do the factors act in combination? Does the effect of one factor depend on the value of the second factor?

Computing an F-ratio for the Interaction will tell us this! Interaction is the key word - remember it for later

Data Types

For our discussion of Anova, we will be using measurement data (numerical scores).

Our Example

You have two independent variables, which defines your groups. Call one factor A and the other B. A has 3 levels and B has 2.

This gives you a matrix of six groups.

	A1	A2	A3
B1	A1B1	A2B1	A3B1
B2	A1B2	A2B2	A3B2

You can get means for A1, A2 or A3 (forgetting about B membership. - Use these for the Main Effect of A.

You can get means for B1 and B2 (forgetting about A membership. - Use these for the Main Effect of B.

You can get 6 means for the 3 x 2 conditions. - Use these for the Interaction of A and B.

So let's get started

An example: College Drinking

You are concerned with college drinking behavior.

You think it is related to your year in school.

You collect data from 1^st year, Sophomores and Juniors. For this example, I don't care about Seniors.

Thus year will be factor A with 3 levels = A1, A2, A3

You think it is also related to gender.

Thus Gender will be factor B with 2 levels = B1, B2

You calculate the means.

Questions?

Do the Years differ? This is the Main Effect of Year - Factor A!

Do the Genders differ? This is the Main Effect of Gender - Factor B!

Does the pattern of the differences between years depend on Gender? This is the Interaction of Year by Gender - the AB interaction!