Functions > Design of Experiments > Factor Screening > Example: ANOVA and Blocking
Example: ANOVA and Blocking
Use the block and anova functions to divide a design matrix into two blocks and to test if the blocking has an effect on the result.
1. Call the fullfact function to create a full factorial design matrix.
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2. Call the block function to divide the design matrix X into two blocks.
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The first eight runs are in Block 1 and the remaining runs are in Block 2.
3. Call the randomize function before carrying out the experiment. The randomization is carried out separately for each block.
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4. Record the experiment results in matrix Y with one row per run of the blocked design matrix B and one column per replicate.
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5. Call the quickscreen function to calculate the effects of the factors, the second order interactions and the blocking.
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6. Use the augment and submatrix functions to extract the factors and their effects from Q, and remove the headers.
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7. Replace the effects by the absolute value of the half effects.
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8. Call the pareto function and then create a Pareto plot.
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Factors A, B, D, interactions AD and BD, and Blocks seem significant.
9. Call the anova function to carry out an analysis of variance. Calculate the critical F-value for the factors, interactions, and blocking. Compare their F-value to the critical F-value.
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10. Use the qF function to calculate the critical F-value for the factors, interactions, and blocking. Compare their F-value to the critical F-value.
Set the level at 5%:
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Set the lowest degree of freedom DF:
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Set the highest degree of freedom DF:
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Factors A, B, D, interactions AD and BD, and Blocks are significant at the 5% level since their F values are greater than Fcrit. This analysis of variance reinforces the subjective conclusion derived from the Pareto plot.
Reference
Montgomery, D.C., Design and Analysis of Experiments, 5th ed., John Wiley & Sons, New York, 2001, pp. 295.
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