Statistical Analysis Professor Richard F. Gunst Department of Statistical Science Lecture 16 Analysis of Data from Unbalanced Experiments

Mason, Gunst, & Hess: Table The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model Error Corrected Total R-Square Coeff Var Root MSE yield Mean Source DF Anova SS Mean Square F Value Pr > F temperature concentration temperatu*concentrat catalyst temperature*catalyst concentrati*catalyst temper*concen*cataly Compare with Table 8.1(c)

Mason, Gunst, & Hess: Table The GLM Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model Error Corrected Total R-Square Coeff Var Root MSE yield Mean Source DF Type I SS Mean Square F Value Pr > F temperature concentration temperatu*concentrat catalyst temperature*catalyst concentrati*catalyst temper*concen*cataly Source DF Type III SS Mean Square F Value Pr > F temperature concentration temperatu*concentrat catalyst temperature*catalyst concentrati*catalyst temper*concen*cataly Compare with Table 8.1(c) Order is Important

The GLM Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model Error Corrected Total R-Square Coeff Var Root MSE yield Mean Source DF Type I SS Mean Square F Value Pr > F temperature concentration catalyst temperatu*concentrat temperature*catalyst concentrati*catalyst Source DF Type III SS Mean Square F Value Pr > F temperature concentration catalyst temperatu*concentrat temperature*catalyst concentrati*catalyst Compare with Table 8.1(c)

Fleet Fuel Comparisons CO 2 Composite Emissions (g/mi) Apparent Conclusion Very Large Difference in Average Emissions Between Conventional and California 150 ppm Sulfur Fuels Apparent Conclusion Very Large Difference in Average Emissions Between Conventional and California 150 ppm Sulfur Fuels

Fleet Fuel Comparisons CO 2 Composite Emissions (g/mi) Correct Conclusion Very Small Difference in Average Emissions Between Conventional and California 150 ppm Sulfur Fuels Correct Conclusion Very Small Difference in Average Emissions Between Conventional and California 150 ppm Sulfur Fuels

Multiple Comparisons Unweighted Averages Should be Avoided Some Averages Have More Data Values than Others Outliers Can be Very Influential LSMEANS for Nonmissing Averages Based on Population Marginal Means Adjust=Bon, Tukey Pdiff

The GLM Procedure Level of Level of yield temperature catalyst N Mean Std Dev 160 c c c c Means Statement LSmeans Statement The GLM Procedure Least Squares Means Adjustment for Multiple Comparisons: Bonferroni LSMEAN temperature catalyst yield LSMEAN Number 160 c c c c Least Squares Means for effect temperature*catalyst Pr > |t| for H0: LSMean(i)=LSMean(j) Dependent Variable: yield i/j

proc glm data=tabl0801; class temperature concentration catalyst; model yield = temperature concentration catalyst temperature*concentration temperature*catalyst concentration*catalyst; means temperature*catalyst / Bon ; lsmeans temperature*catalyst / adjust=Bon pdiff=all ; run;