1. 1 Two-Way ANOVA Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of Networking and Multimedia

2. Scenarios To observe if effects of factors in the following scenarios are significant – –Ratings of music compressed by MP3 compressors: brands vs. ages of the subjects – –Performance of Teaching: methods (Lectures, group studying, and computer assisted instruction) vs. genders of undergraduate students 2

3. Teaching Methods vs. Gender: Knowing only Overall Mean GenderCAILecture Group Studying Mean Boys50 Girls50 Mean50

4. Teaching Methods vs. Gender: Knowing Overall Mean and Row Effects GenderCAILecture Group Studying Mean Boys40 Girls60 Mean50

5. Teaching Methods vs. Gender: Knowing Overall Mean, Row Effects, and Column Effects GenderCAILecture Group Studying Mean Boys50403040 Girls70605060 Mean60504050

6. Teaching Methods vs. Gender: Including Interaction Terms GenderCAILecture Group Studying Mean Boys65401540 Girls55606560 Mean60504050

7. Comparing Four MP3 Compressors Test four brands, A, B, C, D 10 subjects, 5 young and 5 senior, each brand (40 in total) to provide a satisfaction rating on a 10-point scale Assume that the rating to each brand is a normal distribution, but all four distributions are with the same variance

8. Sample Data ABCDMean Young Subjects 1~44572 5.05 5~84581 9~125672 13~165693 17~206763 Mean4.85.87.42.2 *Adapted from: G. R. Norman and D. L. Streiner, Biostatistics, 3rd ed.

9. Sample Data ABCDMean Senior Subjects 21~243634 3.70 25~284425 29~324524 33~363624 37~404333 Mean3.64.82.44.0 *Adapted from: G. R. Norman and D. L. Streiner, Biostatistics, 3rd ed. ABCDMean Brand Mean4.25.34.93.14.375

10. Sum of Squares (Young/Senior)

11. Sum of Squares (Brands)

12. Sum of Squares (Within)

13. Sum of Squares (Total)

14. Sum of Squares (Interactions)

15. Sum of Squares (Total)

16. Expected Values of Sum of Squares

17. Degrees of Freedom

18. Two-way ANOVA Summary SourceSum of Squares dfMean square F Brand 27.87539.2911.99 Young/ Senior 18.225118.2323.52 Brand X Y/S 58.475319.4925.15 Within 24.80320.78 Total 129.37539

19. Hypothesis Testing

20. Histogram of Means

21. Effect of Interaction

22. Possible Types of Interactions

23. de Groot’s Experiment (1965) Observed the ability of chess masters and novices to recall piece positions Experts – –Recalled about 90% of the pieces in a typical mid- game Novices – –Recalled about 20% Many factors might have been introduced Randomized piece positions – –Everybody recalled about 20% – –No effect of expertise

24. Interpretation by Adjusted Data