4/2/2021

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