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Latin and Graeco -Latin Squares

Latin and Graeco -Latin Squares

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Latin and Graeco -Latin Squares

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Presentation Transcript

  1. Latin and Graeco-Latin Squares What we give up to do Exploratory Designs

  2. Hicks Tire Wear Example data

  3. Linear Model

  4. ANOVA with Main Effects

  5. It’s an orthogonal design so… The Type III tests on top match the Type I tests below. Main Effects Are not confounded with each other.

  6. We are primarily interested in Brand, but what about interactions? If we put in even one interaction, then there are no df for error and this Interaction is completely confounded with Brand.

  7. Notice • One cannot estimate and test Interaction terms since we do not have enough d.f. • Interaction terms are confounded with error and other terms. • As we shall see later with Fractional Factorials, they are likely confounded with each other too.

  8. Brand is the only Fixed Effect for Inference

  9. Tukey HSD on Tire Wear LS Means

  10. Residuals vs. Predicted

  11. Normal Plot of Residuals

  12. Normality Test

  13. Hicks Graeco-Latin Square Example

  14. Basic ANOVA with Main Effects

  15. Only Time is close to significance so…

  16. Since this is a screening design….. • Which variables might we investigate further? • How might we collect more data? • What about diagnostics on the model we fit?

  17. Residuals Vs. Predicted Plot

  18. Normality Plot

  19. Normality Test

  20. What happened with our Diagnostics? • With Diagnostics we use Residuals as surrogates for Experimental Error in our Model • The Diagnostics are based on the assumption that our Residuals are independently distributed • This assumption was never true in an absolute sense • However, if the df for Error is “large” relative to the Model df, it is close enough to “true” so that our Diagnostics make sense • Remember, these designs are meant to screen factors for further study