2/13/2008
ANOVA for a randomized block design
- Blocks are used to guarantee uniform or homogeneous groups on the k different treatments
- Randomization is carried out separately within each block
- Model
- Hypotheses
- Sum of Squares Identity
ANOVA table for a randomized block design
| Source of Variation |
d.f. |
Sum of Squares |
Mean Square |
F-Statistic |
p-value |
Treatments
|
k-1 |
SSTr |
MSTr |
MSTr/MSE |
|
| Blocks |
l-1 |
SSBl |
MSBl |
|
|
| Error |
(k-1)(l-1) |
SSE |
MSE |
|
|
| Total |
kl-1 |
SSTO |
|
|
|
- F-distributions: percentiles and p-value can be obtained from statistical software
Example - See SeedSource.sas
Assumptions
- Normality
- Independence
- Equal standard deviations
Residual plots for checking assumptions
- Residual = observation minus estimated mean
- Plot residuals against predicted values (treatment means) and other available variables
- Construct a normal probability plot for the residuals
Multiple Comparisons are used to identify significant differences in the treatments
Nonparametric Alternative
- Friedman Test
- See Bball.mtw (rounding first base)