1. Fixed effects analysis in a Two–way ANOVA

2. Problem 5.6 Layout

3. Crossing and Nesting, Balanced Phosphor Type and Glass Type (the main effects) are crossed For example, Phosphor Type 1 means the same thing regardless of Glass Type Since main effects are crossed we can check for interaction Experimental units are nested within combinations of Phosphor Type and Glass Type Experimental unit 1 for one combination of Phosphor Type and Glass Type does not mean the same thing as Experimental unit 1 for a different combination of Phosphor Type and Glass Type Since there are three observations for each cell the design is balanced

4. Linear Model

5. Problem 5.6 ANOVA Effect Tests Source DF Sum of Squares F Ratio Prob > F Phos. Type2 933.33 8.8421 0.0044* Glass Type1 14450.0 273.78 <.0001* Phos. Type*Glass Type2 133.333 1.2632 0.3178

6. Interaction Plot

7. Phosphorous Type

8. Tukey HSD Level Least Sq Mean 2 A 273.33333 1 B 260.00000 3 B 256.66667 Levels not connected by same letter are significantly different.

9. Glass Effect Plot

10. Residuals and Normality Plot

11. Residuals by Predicted

12. Problem 5.10 Layout

13. Crossed and Nested Temperature and Glass are crossed Can check for Interaction Experimental units are Nested within Treatment combinations There are three observations per cell so the design is balanced

14. Linear Model

15. Problem 5.10 Source DF Sum of Squares F Ratio Prob > F Glass Type 2 150864.5 206.3706 <.0001* Temp. 2 1970334.5 2695.259 <.0001* Glass *Temp. 4 290551.7 198.7257 <.0001* Error 18 2418330.1

16. Interaction Plot

17. LS Means Table (usually put in appendix) LevelLeast Sq Mean Std Error 1, 100572.666711.038093 1, 1251087.333311.038093 1, 1501386.000011.038093 2, 100553.000011.038093 2, 1251035.000011.038093 2, 1501313.000011.038093 3, 100573.3333 11.038093 3, 1251054.666711.038093 3, 150886.666711.038093

18. Now this is slick… LevelLeast Sq Mean 1, 150A 1386.0000 2, 150 B 1313.0000 1, 125 C 1087.3333 3, 125 C 1054.6667 2, 125 C 1035.0000 3, 150 D 886.6667 3, 100 E573.3333 1, 100 E572.6667 2, 100 E553.0000 Levels not connected by same letter are significantly different.

19. Residuals by Predicted

20. Residual Plot and Normality Plot

21. Normality test Shapiro-Wilk W Test W Prob<W 0.966954 0.5237 Note: Ho = The data is from the Normal distribution. Small p-values reject Ho.