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2 k r Factorial Designs

2 k r Factorial Designs. Overview. Computation of Effects Estimation of Experimental Errors Allocation of Variation. 2 k r Factorial Designs. r replications of 2 k Experiments Þ 2 k r observations. Þ Allows estimation of experimental errors. Model: e = Experimental error.

luke-hubbard
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2 k r Factorial Designs

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  1. 2kr Factorial Designs

  2. Overview • Computation of Effects • Estimation of Experimental Errors • Allocation of Variation

  3. 2kr Factorial Designs • r replications of 2k ExperimentsÞ 2kr observations.Þ Allows estimation of experimental errors. • Model: • e = Experimental error

  4. Computation of Effects Simply use means of r measurements • Effects: q0= 41, qA= 21.5, qB= 9.5, qAB= 5.

  5. Estimation of Experimental Errors • Estimated Response: Experimental Error = Estimated - Measured åi,j eij = 0 • Sum of Squared Errors:

  6. Experimental Errors: Example • Estimated Response: • Experimental errors:

  7. Allocation of Variation • Total variation or total sum of squares:

  8. Derivation • Model: Since x's, their products, and all errors add to zero Mean response:

  9. Derivation (Cont) Squaring both sides of the model and ignoring cross product terms:

  10. Derivation (Cont) Total variation: One way to compute SSE:

  11. Example 18.3: Memory-Cache Study

  12. Example 18.3 (Cont) Factor A explains 5547/7032 or 78.88% Factor B explains 15.40% Interaction AB explains 4.27% 1.45% is unexplained and is attributed to errors.

  13. Summary • Replications allow estimation of measurement errors Confidence Intervals of parameters Confidence Intervals of predicted responses • Allocation of variation is proportional to square of effects

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