4/1/2026

Questions on block designs and the material in Chapter 6?

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

• Potato Exercises (See TwoWay-Ex.doc and Potato.R), 7.38 on p. 339

Please complete your reading of Chapter 7 for class on Monday.