Lecture 3: Two-factor ANOVA
Two Way ANOVA
Has two categorical predictors
Two-factor ANOVAs test hypotheses about mean differences in situations where we have more than one
factor (categorical predictor)
We are testing 3 different null hypotheses;
Main effect of A: There is no overall difference between levels of A
Main effect of B: There is no overall difference between levels of B
Interaction between A and B: The difference between levels of A does not depend on level of B (same
as saying: The difference between levels of B does not depend on level of A).
GLM equation
Estimation questions
Interaction term: measures the extent to which observed effect of one factor depends on the
other factor
is the mean score for each “cell” (combination of the levels of the factor)
The interaction terms add up to 0 across each factor (rows and columns)
Degrees of freedom
Main effects: dfA / dfB = number of levels -1
E df b f ti i t b f ll (l l A l l B)
Two Way ANOVA
Has two categorical predictors
Two-factor ANOVAs test hypotheses about mean differences in situations where we have more than one
factor (categorical predictor)
We are testing 3 different null hypotheses;
Main effect of A: There is no overall difference between levels of A
Main effect of B: There is no overall difference between levels of B
Interaction between A and B: The difference between levels of A does not depend on level of B (same
as saying: The difference between levels of B does not depend on level of A).
GLM equation
Estimation questions
Interaction term: measures the extent to which observed effect of one factor depends on the
other factor
is the mean score for each “cell” (combination of the levels of the factor)
The interaction terms add up to 0 across each factor (rows and columns)
Degrees of freedom
Main effects: dfA / dfB = number of levels -1
E df b f ti i t b f ll (l l A l l B)
