Fixed effects analysis in a Two–way ANOVA

Problem 5.6 Layout

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

Linear Model

Problem 5.6 ANOVA Effect Tests Source DF Sum of Squares F Ratio Prob > F Phos. Type * Glass Type <.0001* Phos. Type*Glass Type

Interaction Plot

Phosphorous Type

Tukey HSD Level Least Sq Mean 2 A B B Levels not connected by same letter are significantly different.

Glass Effect Plot

Residuals and Normality Plot

Residuals by Predicted

Problem 5.10 Layout

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

Linear Model

Problem 5.10 Source DF Sum of Squares F Ratio Prob > F Glass Type <.0001* Temp <.0001* Glass *Temp <.0001* Error

Interaction Plot

LS Means Table (usually put in appendix) LevelLeast Sq Mean Std Error 1, , , , , , , , ,

Now this is slick… LevelLeast Sq Mean 1, 150A , 150 B , 125 C , 125 C , 125 C , 150 D , 100 E , 100 E , 100 E Levels not connected by same letter are significantly different.

Residuals by Predicted

Residual Plot and Normality Plot

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