Statistical Analysis

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Statistical Analysis

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

2
Mason, Gunst, Hess
Table 8.1 2  
The ANOVA Procedure   Dependent
Variable yield  
Sum of Source DF
Squares Mean Square F Value Pr gt F   Model
6 1682.400000
280.400000 46.73 0.0047   Error
3 18.000000
6.000000   Corrected Total 9
1700.400000     R-Square Coeff
Var Root MSE yield Mean  
0.989414 3.912923 2.449490
62.60000     Source DF
Anova SS Mean Square F Value Pr gt
F   temperature 1 1440.000000
1440.000000 240.00 0.0006 concentration
1 64.066667 64.066667
10.68 0.0469 temperatuconcentrat 1
41.666667 41.666667 6.94
0.0780 catalyst 1
194.400000 194.400000 32.40
0.0107 temperaturecatalyst 1
0.000000 0.000000 0.00
1.0000 concentraticatalyst 1
0.000000 0.000000 0.00
1.0000 temperconcencataly 0
0.000000 . . .
Compare with Table 8.1(c)
3
Mason, Gunst, Hess
Table 8.1 6  
The GLM Procedure   Dependent
Variable yield  
Sum of Source DF
Squares Mean Square F Value Pr gt F   Model
6 1682.400000
280.400000 46.73 0.0047   Error
3 18.000000
6.000000   Corrected Total 9
1700.400000     R-Square Coeff
Var Root MSE yield Mean  
0.989414 3.912923 2.449490
62.60000     Source DF
Type I SS Mean Square F Value Pr gt
F   temperature 1 1440.000000
1440.000000 240.00 0.0006 concentration
1 64.066667 64.066667
10.68 0.0469 temperatuconcentrat 1
41.666667 41.666667 6.94
0.0780 catalyst 1
21.878788 21.878788 3.65
0.1522 temperaturecatalyst 1
114.502165 114.502165 19.08
0.0222 concentraticatalyst 1
0.285714 0.285714 0.05
0.8413 temperconcencataly 0
0.000000 . . .     Source
DF Type III SS Mean
Square F Value Pr gt F   temperature
1 1120.666667 1120.666667 186.78
0.0008 concentration 1
40.333333 40.333333 6.72
0.0809 temperatuconcentrat 1
8.333333 8.333333 1.39
0.3236 catalyst 1
14.516129 14.516129 2.42
0.2177 temperaturecatalyst 1
85.333333 85.333333 14.22
0.0326 concentraticatalyst 1
0.285714 0.285714 0.05
0.8413 temperconcencataly 0
0.000000 . . .
Order is Important
Compare with Table 8.1(c)
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The GLM
Procedure   Dependent Variable yield  
Sum of Source
DF Squares Mean Square F
Value Pr gt F   Model 6
1682.400000 280.400000 46.73
0.0047   Error 3
18.000000 6.000000   Corrected Total
9 1700.400000     R-Square
Coeff Var Root MSE yield Mean  
0.989414 3.912923 2.449490
62.60000     Source DF
Type I SS Mean Square F Value Pr gt
F   temperature 1 1440.000000
1440.000000 240.00 0.0006 concentration
1 64.066667 64.066667
10.68 0.0469 catalyst 1
16.351351 16.351351 2.73
0.1973 temperatuconcentrat 1
47.194103 47.194103 7.87
0.0676 temperaturecatalyst 1
114.502165 114.502165 19.08
0.0222 concentraticatalyst 1
0.285714 0.285714 0.05
0.8413     Source DF Type
III SS Mean Square F Value Pr gt
F   temperature 1 736.3333333
736.3333333 122.72 0.0016 concentration
1 40.0000000 40.0000000
6.67 0.0816 catalyst 1
2.5714286 2.5714286 0.43
0.5594 temperatuconcentrat 1
8.3333333 8.3333333 1.39
0.3236 temperaturecatalyst 1
85.3333333 85.3333333 14.22
0.0326 concentraticatalyst 1
0.2857143 0.2857143 0.05 0.8413
Compare with Table 8.1(c)
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Fleet Fuel Comparisons
CO2 Composite Emissions (g/mi)
Apparent Conclusion Very Large Difference in
Average Emissions Between Conventional and
California 150 ppm Sulfur Fuels
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Fleet Fuel Comparisons
CO2 Composite Emissions (g/mi)
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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
• AdjustBon, Tukey
• Pdiff

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proc glm datatabl0801 class temperature
concentration catalyst model yield
temperature concentration catalyst
temperatureconcentration temperaturecatalyst
concentrationcatalyst means
temperaturecatalyst / Bon lsmeans
temperaturecatalyst / adjustBon pdiffall run