3/25/2022
Problem Session
Twoway 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
 Twoway ANOVA table
Source of Variation 
d.f. 
Sum of Squares 
Mean Square 
FStatistic 
pvalue 
Factor A main effects 
k1 
SSA 
MSA 
MSA/MSE 

Factor B main effects 
l1 
SSB 
MSB 
MSB/MSE 

Interaction (A*B) 
(k1)(l1) 
SSAB 
MSAB 
MSAB/MSE 

Error 
kl(m1) 
SSE 
MSE 


Total 
klm1 
SSTO 



 Fdistributions: percentiles and pvalue 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 TwoWayEx.doc and Potato.R), 7.38 on p. 339
Please read sections 7.2, 7.3, and 7.4 for class on Monday.