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Quiz 5

# Quiz 5 - God I hate stats In a factorial experiment each...

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God I hate stats. In a  factorial experiment , each possible combinations of the  levels of the factors in each replicate of the experiment is  investigated. An experiment with two factors (A, B) is represented  by a flat sheet in 3-D surface plot. Factorial experiments are the only way to  discover interactions between variables . 2 k  factorial design provides the smallest # of runs for which k  factors can be studied in a complete factorial design. 2 2  Design (A,B factors):  b,ab are similar Main effect of A: Main effect of B: AB interaction: For the above 3 equations, quantities in brackets are  contrasts. Sums of squares  formulas: SS calculated “as usual” with 4n-1 DF, SS E  with 4(n-1) DF with  subtraction. Formulas for Two-Level Factorial with k factors Each at Two Levels and N total Trials V(Effect)= Coefficient = effect/2 =SS E /(4n-4) Residuals:  2 k  Design for k>=3 Factors Effects are calculated the same way as before (average of  some factor at high minus average of some factor at low)

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