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ENMA 420-520 Lecture 12b Slides

# ENMA 420-520 Lecture 12b Slides - Statistical Concepts for...

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Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #12b Analysis of Variance 11

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10/17/09 Summary One-Factor Designs Randomized Block Designs Two-Factor Factorial Experiments Multiple Comparisons of Treatment Means Checking Assumptions 22
10/17/09 Analysis of Variance Determine sources of variation Simplest form: a statistical test of whether the means of several groups are all equal Generalizes t-test to more than two groups 33

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10/17/09 Assigned Variations (single-factor experiment, two treatments) Within-Sample Variation Numerator is the SSE (sum of squared errors) and measures variability not explained by differences between sample means Between-Sample Variation 44 l 2 = σ ll l1 − −− 1 l 2 l 1 l = 1 + σ ll l2 − −− 2 l 2 l 2 l = 1 l 1 + − 2 2 = ° y ° 1 + − 2 2 l 2 = 1 ll l1 − −− 1 l 2 + − 2 ll l2 − −− 2 l 2 2 1 = ± 1
10/17/09 One Factor Completely Randomized Experiments 55 Model andFtestforaCompletely RandomizedDesignwithpTreatments : CompleteModel l ll l = − 0 + − 1 l 1 + − 2 l 2 + ⋯+ − −− 1 l l 1 w : here −− 1 = − 1 if treatment 0 if not n H 0 : 1 = − 2 = ⋯= − −− 1 = 0 ( . . ) i e all meansareequal H a : At least oneof the β ( . . ) parametersdiffersfrom0 i e at least twomeansdiffer : Test Statistic −= MS ( Model ) MSE : Rejectionregion > F F α wherethed istributionof F isbasedon ν 1 = ( p – ) 1 degreesof freedomand ν 2 = ( n – ) p degreesof freedom : Assumptions . 1 All ppopulationprobabilitydistributionscorrespondingtotheptreatmentsare norma . l . 2 . Thepopulationvariancesof thep treatmentsareequal

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10/17/09 Exercise 14.6 Using Excel Data Analysis 66 Traditional Advanced Aeroderiv Anova: Single Factor 14622 9722 16243 13196 10481 14628 SUMMARY 11948 9812 12766 Groups Count Sum Average Variance 11289 9669 8714 Traditional 39 450219 11544.08 1636565 11964 9643 9469 Advanced 21 205050 9764.286 407690.9 10526 9115 11948 Aeroderiv 7 86182 12311.71 7032314 10387 9115 12414 10592 11588 10460 10888 ANOVA 10086 9738 Source of Variation SS df MS F P-value F crit 14628 9295 Between Groups 55360021.96 2 27680011 15.74165 2.75E-06 4.953024 13396 9421 Within Groups 112537186.5 64 1758394 11726 9105 11252 10233 Total 167897208.4 66 12449 10186 11030 9918 10787 9209 10603 9532 10144 9933 11674 9152 11510 9295 10946 10508 Data Continues This is the input range for the ANOVA function
10/17/09 Exercise 14.6 (Cont’d) 77

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10/17/09 Exercise 14.12 88
10/17/09 Exercise 14.12 (Cont’d) 99

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10/17/09 Exercise 14.12 (Cont’d) 1010
10/17/09 Exercise 14.12 (Cont’d) 1111

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10/17/09 Exercise 14.12 (Cont’d) 1212
10/17/09 Randomized Block Designs 1313

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ENMA 420-520 Lecture 12b Slides - Statistical Concepts for...

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