Lec 06 - Sig with One Rep

# Lec 06 - Sig with One Rep - WHAT EFFECTS ARE SIGNIFICANT in...

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WHAT EFFECTS ARE SIGNIFICANT in 2 k Factorial Experiments with only one Replicate? Model Y b b x b x b x N o Y = + + + + + + 1 1 2 2 12 12 2 0 ... ... ( , ) ε σ Significance of b’s rests on estimate of Y 2 Which b’s are significantly different than 0? How to estimate σ Y 2 with no replicates?

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Significance of Factors in 2 k Factorial Designs with One Replicate (# factors > 3) METHOD 1: NORMAL PROBABILITY PLOT Null Hypothesis: H 0 : E i =0 for all i Under H 0 all E's are normally distributed with mean 0 and variance 4 2 σ Y N / Make normal probability plot of E's. If the points are all iid normal accept null hypothesis. 2
If some E's are outliers, then these are significant effects. 3

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Significance of Factors in 2 k Factorial Designs with One Replicate (k>3) METH 2: ASSUME HIGH ORDER FFECTS 0 Let set H contains 3-way and higher order effects. (H is for higher) ex: For a 2 4 factorial experiment H E E E E E = { , , , , } 123 124 134 234 1234 Assume 3-way and higher order effects are
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Lec 06 - Sig with One Rep - WHAT EFFECTS ARE SIGNIFICANT in...

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