Chapter 13 Outline Section 2

Chapter 13 Outline Section 2 - II Section 13.2 Analysis of...

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II. Section 13.2: Analysis of Variance and the Completely Randomized Design (CRD) A. Hypothesis to be Tested 1. H o : μ 1 = μ 2 = … = μ k H 1 : not all μ ’s are equal 2. Example: H o : μ 1 = μ 2 = μ 3 H 1 : not all μ ’s are equal a. The null states that there are no differences in the three methods when comparing the average number of systems assembled. (i.e.: there are no treatment effects) b. The alternative states that there is a treatment effect. (at least one method differs in number of systems assembled)
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B. Data Format and Notation: 1. Number of Treatments (k) (k=3 assembly methods) 2. X ij = i th obs in the j th treatment 3. n j = size for the j th treatment 4. j X = mean of j th treatment 5. = = j i i T n n 1 6. T n i ij k j n X GrandMean X j = = = = 1 1
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Method A Method B Method C X 11 = 58 X 12 = 58 X 13 = 48 X 21 = 64 X 22 = 69 X 23 = 57 X 31 = 55 X 32 = 71 X 33 = 59 X 41 = 66 X 42 = 64 X 43 = 47 X 51 = 67 X 52 = 68 X 53 = 49 n 1 = 5 n 2 = 5 n 3 = 5 1 X =62 2 X =66 3 X = 52 2 1 S = 27.5 2 2 S = 26.5 2 3 S = 31.0 n T = n 1 + n 2 + n 3 = 5+5+ 5 = 15 7. The following plot gives a graphical display of the data by sample.
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