Functions > Design of Experiments > Factor Screening > Example: ANOVA for Unreplicated Factorials
Example: ANOVA for Unreplicated Factorials
Use the anova function to carry out an analysis of variance for an unreplicated factorial by detecting a nonsignificant factor and then projecting the factorial into a lower-order factorial.
1. Call the fullfact function to construct a full factorial design matrix for an experiment testing the filtration rate of a pilot plant. The factors A, B, C, and D stand for the temperature, the pressure, the concentration of formaldehyde, and the stirring rate, respectively.
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2. Record the results of the experiment in matrix Y1 with one element per each of the sixteen runs.
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3. Call the quickscreen function to get the mean response for each main factor.
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4. Create an effects plot to determine the significant factors.
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Factor C and the second-order interactions involving C have only a small effect on the experiment. Compared to factors A, B and D, factor C is not significant.
5. Call the anova function to carry out an analysis of variance.
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The anova function returns an error because Y1 is unreplicated. However, since C is not significant, “Run 1” and "Run 5" are duplicates as far as factors A, B, and D are concerned. This is also the case for “Run 2" and "Run 6". In fact, the whole ABCD 24 design matrix contains a duplicate of the ABD 23 design matrix when C is not significant.
6. Call the fullfact function to create a 23 full factorial design matrix.
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In X2, the factor names are changed. The initial factors A, B, D become A, B, C.
7. Rearrange the experiment results to fit a 23 full factorial experiment.
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8. Call the anova function using Y2.
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9. Use the qF function to calculate the critical F-value for the factors and interactions and compare their F-value to the critical F-value.
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The effect plot shows that factor C is not significant compared to A, B, and D.
Factors A, B, D (shown in V as A, B, C) and their interactions AD, BD (shown in V as AC, BC) 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 effects plot.
Reference
Montgomery, D.C., Design and Analysis of Experiments, 5th ed., John Wiley & Sons, New York, 2001, pp. 246.
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