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The General 2k Factorial Design

2. General Procedure for a 2k Factorial Design. Estimate factor effects (sign

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The General 2k Factorial Design

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    1. 1 The General 2k Factorial Design Section 6-4, pg. 242, Table 6-9, pg. 243 There will be k main effects, and

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    3. 3 Unreplicated 2k Factorial Designs These are 2k factorial designs with one observation at each corner of the “cube” An unreplicated 2k factorial design is also sometimes called a “single replicate” of the 2k These designs are very widely used Risks…if there is only one observation at each corner, is there a chance of unusual response observations spoiling the results? Modeling “noise”?

    4. 4 Spacing of Factor Levels in the Unreplicated 2k Factorial Designs

    5. 5 Unreplicated 2k Factorial Designs Lack of replication causes potential problems in statistical testing Replication admits an estimate of “pure error” (a better phrase is an internal estimate of error) With no replication, fitting the full model results in zero degrees of freedom for error Potential solutions to this problem Pooling high-order interactions to estimate error Normal probability plotting of effects (Daniels, 1959) Other methods…see text, pp. 246

    6. 6 Example of an Unreplicated 2k Design A 24 factorial was used to investigate the effects of four factors on the filtration rate of a resin The factors are A = temperature, B = pressure, C = mole ratio/concentration, D= stirring rate Experiment was performed in a pilot plant

    7. 7 The Resin Plant Experiment

    8. 8 The Resin Plant Experiment

    9. 9 Estimates of the Effects

    10. 10 The Normal Probability Plot of Effects

    11. 11 The Half-Normal Probability Plot

    12. 12 ANOVA Summary for the Model

    13. 13 The Regression Model

    14. 14 Model Residuals are Satisfactory

    15. 15 Model Interpretation – Interactions

    16. 16 Model Interpretation – Cube Plot

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    19. 19 Model Interpretation – Response Surface Plots

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