University:
California State University, Northridge
Course:
ME 296A-Z | Experimental Topics Courses in Mechanical Engineering
Academic year:

2024
Views:

225

Pages:

19
Author:

Rex Calderon

13-4: Randomized Complete Block Designs 13-4.1 Design and Statistical Analyses The randomized block design is an extension of the paired t-test to situations where the factor of interest has more than two levels. Figure 13-9 A randomized complete block design. 13-4: Randomized Complete Block Designs 13-4.1 Design and Statistical Analyses For example, consider the situation of Example 10-9, where two different methods were used to predict the shear strength of steel plate girders. Say we use four girders as the experimental units. 41 13-4: Randomized Complete Block Designs 13-4.1 Design and Statistical Analyses General procedure for a randomized complete block design: 42 13-4: Randomized Complete Block Designs 13-4.1 Design and Statistical Analyses The appropriate linear statistical model: We assume • treatments and blocks are initially fixed effects • blocks do not interact • 43 13-4: Randomized Complete Block Designs 13-4.1 Design and Statistical Analyses We are interested in testing: 44 13-4: Randomized Complete Block Designs 13-4.1 Design and Statistical Analyses The mean squares are: 45 13-4: Randomized Complete Block Designs 13-4.1 Design and Statistical Analyses The expected values of these mean squares are: 46 13-4: Randomized Complete Block Designs 13-4.1 Design and Statistical Analyses Definition 47 13-4: Randomized Complete Block Designs 13-4.1 Design and Statistical Analyses 48 13-4: Randomized Complete Block Designs Example 13-5 49 13-4: Randomized Complete Block Designs Example 13-5 50 13-4: Randomized Complete Block Designs Example 13-5 51 13-4: Randomized Complete Block Designs Example 13-5 52 13-4: Randomized Complete Block Designs Minitab Output for Example 13-5 53 13-4: Randomized Complete Block Designs 13-4.2 Multiple Comparisons Fisher’s Least Significant Difference for Example 13-5 Figure 13-10 Results of Fisher’s LSD method. 54 13-4: Randomized Complete Block Designs 13-4.3 Residual Analysis and Model Checking Figure 13-11 Normal probability plot of residuals from the randomized complete block design. 55 13-4: Randomized Complete Block Designs Figure 13-12 Residuals by treatment. 56 13-4: Randomized Complete Block Designs Figure 13-13 Residuals by block. 57 13-4: Randomized Complete Block Designs Figure 13-14 Residuals versus ŷij. 58

Randomized Complete Block Design

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