1. Fixed effects analysis in a Two–way ANOVA

2. 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

3. Interaction Plot

4. Phosphorous Type

5. Tukey HSD LevelLeast Sq Mean 2A 273.33333 1 B260.00000 3 B256.66667 Levels not connected by same letter are significantly different.

6. Glass Effect Plot

7. Residuals and Normality Plot

8. Residuals by Predicted

9. 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*

10. Interaction Plot

11. 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.

12. Residuals by Predicted

13. Residual Plot and Normality Plot

14. 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.