3/24/2023
Problem Session
Two-way ANOVA (Sec 7.1R, Sec7.2R, and Sec 7.3R)
- Hypothetical Exeperiment
- Is student performance in the introductory statistics course affected by the teaching method and/or the particular instructor teaching the course?
- Model
- Interaction
- Profile plots (See handout and make decisions on effects)
- Plot of the cell means against the levels of Factor A and follow (profile) the levels of Factor B
- Plot of the cell means against the levels of Factor B and follow (profile) the levels of Factor A
- Hypotheses
- Sum of Squares Identity
- SSTO = SSA + SSB + SSAB + SSE
- Two-way ANOVA table
| Source of Variation |
d.f. |
Sum of Squares |
Mean Square |
F-Statistic |
p-value |
Factor A main effects |
k-1 |
SSA |
MSA |
MSA/MSE |
|
| Factor B main effects |
l-1 |
SSB |
MSB |
MSB/MSE |
|
| Interaction (A*B) |
(k-1)(l-1) |
SSAB |
MSAB |
MSAB/MSE |
|
| Error |
kl(m-1) |
SSE |
MSE |
|
|
| Total |
klm-1 |
SSTO |
|
|
|
- F-distributions: percentiles and p-value can be obtained from statistical software
- 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 can be used to identify significant differences in the treatments
In class exercises for Monday
- 6.38 on p. 298, Potato Exercises (See TwoWay-Ex.doc and Potato.R), 7.38 on p. 339
Please read Sections 7.2, 7.3, and 7.4 for class on Monday.