Topic6

# Topic6 - ANOVA Graphical Cereal Example nknw677.sas Y =...

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ANOVA: Graphical

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Cereal Example: nknw677.sas Y = number of cases of cereal sold (CASES) X = design of the cereal package (PKGDES) r = 4 (there were 4 designs tested) ni = 5, 5, 4, 5 (one store had a fire) nT = 19
Cereal Example: input data cereal; infile 'I:\My Documents\Stat 512\CH16TA01.DAT' ; input cases pkgdes store; proc print data =cereal; run ; Obs cases pkgdes store Obs cases pkgdes store 1 11 1 1 11 23 3 1 2 17 1 2 12 20 3 2 3 16 1 3 13 18 3 3 4 14 1 4 14 17 3 4

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Cereal Example: Scatterplot title1 'Types of packaging of Cereal' ; title2 'Scatterplot' ; symbol1 v =circle i = none ; proc gplot data =cereal; plot cases*pkgdes; run ;
Cereal Example: ANOVA proc glm data =cereal; class pkgdes; model cases=pkgdes/ xpx inverse solution ; means pkgdes; run ; Class Level Information Class Levels Values pkgdes 4 1 2 3 4 Means statement output Level of

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Cereal Example: Means proc means data =cereal; var cases; by pkgdes; output out =cerealmeans mean =avcases; proc print data =cerealmeans; Obs pkgdes _TYPE_ _FREQ_ avcases 1 1 0 5 14.6 2 2 0 5 13.4 3 3 0 4 19.5 4 4 0 5 27.2 title2 'Scatterplot of means' ;
Cereal Example: Means (cont)

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ANOVA Table Source of Variation df SS MS Model (Regressio n) r – 1 Error nT – r Total nT – 1 M SSM df E SSE df 2 i i. .. i n (Y Y ) - 2 ij i. i j (Y Y ) - ∑∑ 2 ij .. i j (Y Y ) - ∑∑
ANOVA test

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Cereal Example: ANOVA table proc glm data =cereal; class pkgdes; model cases=pkgdes; run ; Sum of Source DF Squares Mean Square F Value Pr > F Model 3 588.2210526 196.0736842 18.59 <.0001 Error 15 158.2000000 10.5466667 Corrected Total 18 746.4210526 R-Square Coeff Var Root MSE cases Mean
Cereal Example: Design Matrix 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 M M M M M M M M M M M M M M M

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Cereal Example: Inverse proc glm data =cereal; class pkgdes; model cases=pkgdes/ xpx inverse solution ; means pkgdes; run ;
Cereal Example: /xpx The X'X Matrix 'X X'Y Y'X Y'Y X

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Cereal Example: /inverse (X'X) (X'Y) X'Y (Y' X)(X'X) Y'Y (Y'X)(X' X) X'Y - - - - -
Cereal Example: /solution Standard

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Cereal Example: ANOVA Means statement output Level of ------------cases------------ pkgdes N Mean Std Dev 1 5 14.6000000 2.30217289 2 5 13.4000000 3.64691651 3 4 19.5000000 2.64575131 4 5 27.2000000 3.96232255
Cereal Example: Means proc means data =cereal printalltypes ; class pkgdes; var cases; output out =cerealmeans

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Topic6 - ANOVA Graphical Cereal Example nknw677.sas Y =...

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