1. Monday, November 15
Analysis of Variance

2. The Analysis of Variance
Monday, November 15
The Analysis of Variance

3. The Analysis of Variance
Monday, November 15
The Analysis of Variance
ANOVA

6. F = Between-group variance estimate within-group variance estimate _
SST =  (X - XG)2
SSB =  Ni (Xi - XG)2
SSW =  (X1 - X1)2 +
 (X2 - X2)2 + ••••
 (Xk - Xk)2
SST = SSB + SSW _ _ _ _ _

7. F = Between-group variance estimate within-group variance estimate
MSB = SSB / dfB
MSW = SSW / dfW
where
dfB = k-1 (k = number of groups)
dfW = N - k

8. Fisher’s Protected t-test
Xi - Xj
MSW ( 1/Ni + 1/Nj) _
Where df = N - k

9. dfB (F - 1)
Est ω =
dfB F + dfW
Est ω bears the same relationship to F that rpb bears to t.

10. The factorial design is used to study the relationship of two or more independent variables (called factors) to a dependent variable, where each factor has two or more levels. - p. 333

11. The factorial design is used to study the relationship of two or more independent variables (called factors) to a dependent variable, where each factor has two or more levels.
In this design, you can evaluate the main effects of each factor independently (essentially equivalent to doing one-way ANOVA’s for each of the factors independently), but you are also able to evaluate how the two (or more factors) interact.

14. Partitioning variation in a 2x2 factorial design.
TOTAL VARIATION
Variation within groups (error)
Variation between groups
Variation
from Factor 1
Variation
from Factor 2
Variation from
Factor 1 x 2 interaction

18. 1.A Compute SST
B. Compute SSB
C. Subtract SSB from SST to obtain SSW (error)
D. Compute SS1
E. Compute SS2
F. Compute SS1x2 by subtracting SS1 and SS2 from SSB
2. Convert SS to MS by dividing SS by the appropriate d.f.
3. Test MS1,MS2 and MS1x2 using F ratio.

20. More advanced ANOVA topics
N-way ANOVA
Repeated Measures designs
Mixed models
Contrasts