Week 2: Analysis of variance (ANOVA)
ANOVA can be done when the independent variables are nominal level and the dependent variable is interval level.
Research question: What is the effect of X1 and X2 on Y?
Check the assumptions of homogeneity of the variances and normality of the residuals.
Homogeneity: Check Levene’s test. If non-significant, then the assumption is violated
Normality: are residuals normally distributed on the histogram? If no, the assumption is violated
What are the group sizes? Discuss robustness of the F tests with respect to possible violations of the assumptions.
If group size is larger than 15, then the F test is robust for non-normality. The F test is robust to unequal group variances if the maximum number of people in a subgroup divided by the minimum number of people is smaller than 1.5.
What are the null and alternative hypotheses to test the ANOVA model?
H0:μ11=μ12=μ21=μ22
Ha: at least two μij not equal
Can the null hypothesis be rejected? If so, which effects are significant?
If the average of different groups is different, the H0 can be rejected. Here report the F statistic with the degrees of freedom and p value. For example: F(3,164) = 12.679,p < .001
How much variance of test score is explained by the total model and by each individual effect?
When we want to know how much variance is explained by the total model we look at R2. This can be seen written at the bottom of the Tests of Between-Subjects Effect table or can be calculated by dividing the Sum of Square (SS) of the corrected model by the Sum of Square of the total.
The individual contribution can be calculated by dividing the SS of the individual coefficient by the SS of the corrected total.
- Example: the SS of a method is 146.720. The SS of the corrected model is 1429.661. We then divide the former by the latter and we get: .103. The way we would mark the contribution of method would be then: η2Method=.102
