ChE253K Spring09 2-Way ANOVA.1

# ChE253K Spring09 2-Way ANOVA.1 - Class Business HW 12 Due...

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1 ChE 253K Lecture 22 Class Business HW 12 Due Friday 5pm in FunLab (CPE 1.420)

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2 ChE 253K Lecture 22 Randomized Block or Two-Way ANOVA Lecture 22 -- Engineering Statistics
3 ChE 253K Lecture 22 Outline Of This Lecture One-Way ANOVA Review ANOVA’s Hypothesis Test Two-Way ANOVA Two-Way To Significance

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4 ChE 253K Lecture 22 This Lecture In The Text Sampling and Experimental Design Ch. 12, Sect. 12.1 One-Way ANOVA Completely Randomized Ch. 12, Sect. 12.2 Two-Way ANOVA Randomized Block Ch. 12, Sect. 12.3
5 ChE 253K Lecture 22 Example: Detergent Gasoline Example on Text p. 422 – 423 Sample = Fuel injectors Observation: “Cleanness” Treatment: Detergents 1, 2, 3, 4 Sources: Observations Det’nt 1 45 43 51 Det’nt 2 47 46 52 Det’nt 3 48 50 55 Det’nt 4 42 37 49

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6 ChE 253K Lecture 22 ANOVA Shopping List 1) Observations & Summary Stats 2) Sums of Squares, Mean Squares, and Degrees of Freedom Total SST Treatment SS(Tr), MS(Tr), ν Tr Blocks SS(Bl), MS(Bl), ν Bl Error SSE, MSE, ν Er 3) Test Stat & Decision
7 ChE 253K Lecture 22 ANOVA Data/Calc Table Observations Sum Stats

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8 ChE 253K Lecture 22 Example Data – One-Way Table Treat/Block Observations Total N Mean Det’nt 1 45 43 51 139 3 46.3 Det’nt 2 47 46 52 145 3 48.3 Det’nt 3 48 50 55 153 3 51.0 Det’nt 4 42 37 49 128 3 42.7 Total 565 12 47.1 obs y ij mean y i mean y
9 ChE 253K Lecture 22 ANOVA Data/Calc Table Total Dev 2 Treatment Dev 2

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10 ChE 253K Lecture 22 Example Data for SST Calculation Treat/Block Eng 1 Eng 2 Eng 3 Total N Mean Det’nt 1 45 43 51 139 3 46.3 Det’nt 2 47 46 52 145 3 48.3 Det’nt 3 48 50 55 153 3 51.0 Det’nt 4 42 37 49 128 3 42.7 Total 182 176 207 565 12 47.1 N 4 4 4 12 Mean 45.5 44.0 51.8 47.1 Total Dev’s = Observations – Overall Mean
11 ChE 253K Lecture 22 Sums of Squares – Total ( 29 ( 29 ( 29 2 1 1 Total Deviation of Sum Sqs Total One & Two-Way 1 1 Degrees of Freedom of 1 1 Mean Squares Total i ij ij ij n a ij i j y y y SST y y N ab SST Observations MST SST N τ υ = = = - = - = = - = - ≡ = - = - = ∑∑ gg mean sq’s = (sum sq’s)/(d’s of f)

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12 ChE 253K Lecture 22 Example Data for SS(Tr) Calculation Treat/Block Eng 1 Eng 2 Eng 3 Total N Mean Det’nt 1 45 43 51 139 3 46.3
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## This note was uploaded on 02/25/2010 for the course CHE 253k taught by Professor Staff during the Spring '08 term at University of Texas at Austin.

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ChE253K Spring09 2-Way ANOVA.1 - Class Business HW 12 Due...

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