ANOVA (analysis of variance) is used to determine if different treatment groups differ significantly on some measure. It compares the variance between groups to the variance within groups. If the between-group variance is large relative to the within-group variance, it suggests the treatment had an effect. The analysis calculates an F-ratio, with larger values indicating it is less likely the groups differ due to chance. Researchers use statistical tables to determine the probability (p-value) that the F-ratio occurred by chance if there was actually no effect.

1. Analyses of Variance (ANOVA’s) A Basic Introduction Florian Schwarz http://florianschwarz.net

13. What are the Odds (III) When 20 of us run the same study, one of us will find a significant difference between groups, EVEN IF THERE ACTUALLY IS NO DIFFERENCE!

14. Calculating Sums of Squares

17. Total Sums of Squares Group 1 Group 2 (mean 5) (mean 15) 232 Total SS 64 8 18 118 Group 2 total SS 36 6 16 9 3 13 9 3 13 114 Group1 total SS 4 -2 8 25 -5 5 36 -6 4 49 -7 3 Squared X – overall mean (10) Score (X)

21. Within Group Sums of Squares Group 1 Group 2 (mean 5) (mean 15) 32 Total Within Group SS 9 3 18 18 Group 2 within group SS 1 1 16 4 -2 13 4 -2 13 14 Group1 within group SS 9 3 8 0 0 5 1 -1 4 4 -2 3 Squared X - group mean Score (X)

22. Between Group Sums of Squares Group 1 Group 2 (mean 5) (mean 15) 5 5 5 5 -5 -5 -5 -5 Group mean – overall mean 200 Total Between Group SS 25 15 18 100 Group 2 contribution to between group SS 25 15 16 25 15 13 25 15 13 100 Group1 contribution to between group SS 25 5 8 25 5 5 25 5 4 25 5 3 Squared group mean Score (X)