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Chapter 2 - Getting Started with Completely Randomized Design 1 Assembling the Research Design Section 2.1pp 37-38 The Bacterial Growth on Stored Meat Problem (Example 2.1) Packaging Condition Log (count/cm ) 2 Total Mean Commercial 7.66, 6.98, 7.80 22.44 7.48 Vacuum 5.26, 5.44, 5.80 16.50 5.50 Mixed Gas 7.41, 7.33, 7.04 21.78 7.26 2 100% CO 3.51, 2.91, 3.66 10.08 3.36 How to Randomize Section 2.2 pp 39-41 Method 1 - Random number tables, cards, dice, etc. This works fine for small experiments and there really is no better. Method 2 - Software is available. These are good for large data sets or complex designs. Here is an example using PROC PLAN of SAS. In the first step we make the experimental units and then in the second stage we randomize it.

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Chapter 2 - Getting Started with Completely Randomized Design 2 This is the unrandomized assignment. This is just the first step. /* The unrandomized design */ data a; do steak=1 to 12; if (steak <= 3) then treat='Commercial'; else if (3 < steak <= 6) then treat='Vacuum'; else if (6 < steak <= 9) then treat='MixedGas'; else if (9 < steak) then treat='100%CO2'; output; end; run; Proc print data=a; run; The SAS System Obs steak treat 1 1 Commercial 2 2 Commercial 3 3 Commercial 4 4 Vacuum 5 5 Vacuum 6 6 Vacuum 7 7 MixedGas 8 8 MixedGas 9 9 MixedGas 10 10 100%CO2 11 11 100%CO2 12 12 100%CO2
Chapter 2 - Getting Started with Completely Randomized Design 3 This is the randomized assignment. This is how the experiment would be conducted. Note that you do both parts (i.e. page 2 and 3 of these notes). /* Randomize the design */ proc plan seed=12345; factors steak=12; output data=a out=b; run; Proc print data=b; run; The PLAN Procedure Factor Select Levels Order steak 12 12 Random ---------------steak--------------- 5 10 11 6 4 3 7 1 8 12 9 2 Obs steak treat 1 5 Commercial 2 10 Commercial 3 11 Commercial 4 6 Vacuum 5 4 Vacuum 6 3 Vacuum 7 7 MixedGas 8 1 MixedGas 9 8 MixedGas 10 12 100%CO2 11 9 100%CO2 12 2 100 % CO2

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Chapter 2 - Getting Started with Completely Randomized Design 4 A Statistical Model for the Experiment Section 2.4 pp 42-47
Chapter 2 - Getting Started with Completely Randomized Design 5 General Linear Statistical Model i y is the response variable and x are the design variables. The design variables can be quantitative (either fixed or covariates) or categorical. The following equations are valid for both. i Note that each of the design variables, x , can be to a power. If treatments are categorical then the design variables are indicator variables . That is the case in the meat example.

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Chapter 2 - Getting Started with Completely Randomized Design 6 We can write the model as. .. What does the model look like for the commercial wrap treatment 1 234 0 where x =1 and x =x =x =0? Note the use of the intercept, \$ , is not needed. the means model comes from this representation since we can say this flexibility also allows the modeling of covariates ij where x is the moisture content of the j steak in the i trt and \$ is th th the linear regression coefficient. This is Analysis of Covariance.
Chapter 2 - Getting Started with Completely Randomized Design 7 Estimation of the Model Parameters with Least Squares Section 2.5 pp 47-50 The least squares method provides the smallest sum of squared

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