One Way ANOVA

1. SStotal SSbetween SSwithin Logic of Two Way ANOVA One Way ANOVA

2. SStotal SSbetween SSwithin SSfactorA SSfactorB SSinteraction Interaction Main Effect 1 Main Effect 2 Logic of Two Way ANOVA Two Way ANOVA

3. This is no surprise This is news Logic of Two Way ANOVA

4. Steps for Two Way ANOVA 50o 70o 90o 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon Step 1: Get the cell means, row means, column means, and grand mean

5. Steps for Two Way ANOVA 50o 70o 90o 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon Step 1: Get the SStotal = 56

6. Steps for Two Way ANOVA 50o 70o 90o 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon Step 2: Get the SSwithin = 14

7. Steps for Two Way ANOVA 50o 70o 90o 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon Step 3: Get the SStime = 18

8. Steps for Two Way ANOVA 50o 70o 90o 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon Step 4: Get the SStemp = 12

9. SStotal SSbetween SSwithin SStime SStemp SSinteraction = 56 = 14 = 18 = 12 Steps for Two Way ANOVA 50o 70o 90o 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon Step 5: Get the SSinteraction = 12

10. Steps for Two Way ANOVA 50o 70o 90o Step 6: Finish the table 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon

11. Steps for Two Way ANOVA 50o 70o 90o Step 6: Finish the table 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon

12. Steps for Two Way ANOVA 50o 70o 90o Step 6: Finish the table 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon

13. Steps for Two Way ANOVA 50o 70o 90o Step 6: Finish the table 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon

14. p < .01 p < .05 p < .05 Steps for Two Way ANOVA 50o 70o 90o Step 6: Finish the table 1 2 3 4 5 6 3 1 2 Morning 1 4 1 0 1 2 0 0 0 Afternoon

15. Steps for Two Way ANOVA Since there are only two levels of time, you know they are significantly different from one another Since there are three levels of temp, you will need to use post-hoc multiple comparisons (e.g. Tukey’s HSD) to determine which levels differ from one another.

16. Steps for Two Way ANOVA To understand the interaction more fully, you might want to look at the “simple effects” You could compute the effect of temp just in the morning, for example. You would simply compute SStemp at AM

17. Assumptions for the Two Factor ANOVA • Observations within each sample are independent. • Populations are normally distributed. • Populations from which the samples are selected must have equal variances (homogeneity of variance). • Equal cell Ns (if calculating by hand)