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Lecture 6.11 © 2015 Michael Stuart Design and Analysis of Experiments Lecture 6.1 1.Review of split unit experiments −Why split? −Why block? 2.Review of.

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Presentation on theme: "Lecture 6.11 © 2015 Michael Stuart Design and Analysis of Experiments Lecture 6.1 1.Review of split unit experiments −Why split? −Why block? 2.Review of."— Presentation transcript:

1 Lecture 6.11 © 2015 Michael Stuart Design and Analysis of Experiments Lecture 6.1 1.Review of split unit experiments −Why split? −Why block? 2.Review of Laboratory 2 −Cambridge grassland experiment −Soup mix packet filling 3.An interesting interaction? 4.Course evaluation 5.Review of 2014 Annual Examination Postgraduate Certificate in Statistics Design and Analysis of Experiments

2 Lecture 6.12 © 2015 Michael Stuart Split units experiments arise when –one set of treatment factors is applied to experimental units, –a second set of factors is applied to sub units of these experimental units. Originated in agriculture where they are referred to as split plot experiments. Whole units may be regarded as blocks "Most industrial experiments are... split plot in their design.“ C. Daniel (1976) p. 175 Postgraduate Certificate in Statistics Design and Analysis of Experiments

3 Lecture 6.13 © 2015 Michael Stuart Why split? Adding another factor after the experiment started Changing one factor is –more difficult –more expensive –more time consuming than changing others Some factors require better precision than others Postgraduate Certificate in Statistics Design and Analysis of Experiments Cambridge grassland Component lifetimes Water resistance Corrosion resistance

4 Lecture 6.14 © 2015 Michael Stuart Why block? Blocking is useful when there are known external factors (covariates) that affect variation between plots. Blocking reduces bias arising due to block effects disproportionately affecting factor effects due to levels disproportionally allocated to blocks. Neighbouring plots are likely to be more homogeneous than separated plots, so that –blocking reduces variation affecting comparisons when treatments are compared within blocks –(precision is increased when results are combined across blocks). Postgraduate Certificate in Statistics Design and Analysis of Experiments

5 Lecture 6.15 © 2015 Michael Stuart Block or Not? Not blocking when there is a block effect implies reduced power for treatment effects test; because Error term includes block variation. Blocking when there is no block effect implies reduced power for treatment effects test; because Error degrees of freedom reduced Postgraduate Certificate in Statistics Design and Analysis of Experiments

6 Lecture 6.16 © 2015 Michael Stuart Design and Analysis of Experiments Lecture 6.1 1.Review of split unit experiments −Why split? −Why block? 2.Review of Laboratory 2 −Cambridge grassland experiment −Soup mix packet filling 3.An interesting interaction? 4.Course evaluation 5.Review of 2014 Annual Examination Postgraduate Certificate in Statistics Design and Analysis of Experiments

7 Lecture 6.17 © 2015 Michael Stuart Laboratory 2, Exercise 1 Cambridge Grassland Experiment 3 grassland treatments Rejuvenator R Harrow H no treatment C randomly allocated to 3 neighbouring plots, replicated in 6 neighbouring blocks 4 fertilisers Farmyard manure F Straw S Artificial fertiliser A no fertiliser C randomly allocated to 4 sub plots within each plot. Postgraduate Certificate in Statistics Design and Analysis of Experiments

8 Lecture 6.18 © 2015 Michael Stuart Cambridge Grassland Experiment Postgraduate Certificate in Statistics Design and Analysis of Experiments

9 Lecture 6.19 © 2015 Michael Stuart Experimental results, Yields in pound (lbs) Postgraduate Certificate in Statistics Design and Analysis of Experiments Block 1Block 2Block 3Block 4Block 5Block 6 CHRCHRCHRCHRCHRCHR A266213208210222266220184 216178207202175184169142151 C1651271551501671631551181531591251351471189813210469 F198180200247203228190168174225149162184175144164145116 S18412715018816715714012814117410711315411211311689101

10 Lecture 6.110 © 2015 Michael Stuart Treatment yields vs Layout yields (Block 1) Postgraduate Certificate in Statistics Design and Analysis of Experiments Block 1 CHR A266213208 C165127155 F198180200 S184127150 Block1 Whole Plot123 TreatmentHCR Sub Plot 1 C 127 A 266 A 208 Sub Plot 2 A 213 S 184 C 155 Sub Plot 3 F 180 C 165 F 200 Sub Plot 4 S 127 F 198 S 150

11 Lecture 6.111 © 2015 Michael Stuart 3-Step Decomposition of Total Variation Step 1: Two components of total variation Step 2: Analysis of whole plot total variation Step 3: Analysis of subplot total variation Postgraduate Certificate in Statistics Design and Analysis of Experiments

12 Lecture 6.112 © 2015 Michael Stuart Units Blocks Whole Plots Subplots Plot Structure Postgraduate Certificate in Statistics Design and Analysis of Experiments

13 Lecture 6.113 © 2015 Michael Stuart Step 1: Two components of total variation Mintab model:Plot Subplot(Plot) Source DF SS MS F P Plot 17 54577.3 3210.4 2.63 0.004 Subplot(Plot) 54 65896.0 1220.3 ** Error 0 * * Total 71 120473.3 Minitab model:Plot Source DF SS MS F P Plot 17 54577 3210 2.63 0.004 Error 54 65896 1220 Total 71 120473 Postgraduate Certificate in Statistics Design and Analysis of Experiments

14 Lecture 6.114 © 2015 Michael Stuart Units Blocks Whole Plots Subplots Step 2: Analysis of whole plot total variation Treatment Factors Treatment Postgraduate Certificate in Statistics Design and Analysis of Experiments ANOVA MS(Blocks) MS(Treatments) MS(Whole Plot Residual) Whole Plot and Treatment Structure

15 Lecture 6.115 © 2015 Michael Stuart Step 2: Analysis of whole plot total variation Minitab model:Block Treatment Source DF SS MS F P Block 5 37425 7485 6.79 0.000 Treatment 2 12471 6236 5.65 0.005 Error 64 70577 1103 Total 71 120473 Minitab model:Plot Source DF SS MS F P Plot 17 54577 3210 2.63 0.004 Error 54 65896 1220 Total 71 120473 Plot Residual DF = 17 – 5 – 2 = 10 Plot Residual SS = 54577 – 37425 – 12471 = 4681 Postgraduate Certificate in Statistics Design and Analysis of Experiments

16 Lecture 6.116 © 2015 Michael Stuart Units Blocks Whole Plots Subplots Whole Plot and Treatment Structure Treatment Factors Treatment ANOVA MS(Blocks) MS(Treatments) MS(Whole Plot Residual) B x T Postgraduate Certificate in Statistics Design and Analysis of Experiments

17 Lecture 6.117 © 2015 Michael Stuart Minitab model:Block Treatment Block*Treatment Source DF SS MS F P Block 5 37425 7485 6.13 0.000 Treatment 2 12471 6236 5.11 0.009 Block*Treatment 10 4681 468 0.38 0.949 Error 54 65896 1220 Total 71 120473 Step 2: Analysis of whole plot total variation Postgraduate Certificate in Statistics Design and Analysis of Experiments

18 Lecture 6.118 © 2015 Michael Stuart Units Blocks Whole Plots Subplots Plot and Treatment Structure Treatment Factors Treatment Fertiliser ANOVA MS(Blocks) MS(Treatments) MS(Whole Plot Residual) B x T MS(Fertiliser) MS(Interactions) MS(Subplot Residual) Postgraduate Certificate in Statistics Design and Analysis of Experiments Subplots

19 Lecture 6.119 © 2015 Michael Stuart Split Plots Analysis Minitab model:B + T + B x T + F + T x F + B x F Source DF SS MS F P B 5 37425.1 7485.0 21.37 0.002 x T 2 12471.0 6235.5 13.32 0.002 B*T 10 4681.1 468.1 1.94 0.079 F 3 56022.7 18674.2 151.24 0.000 T*F 6 781.5 130.3 0.54 0.774 B*F 15 1852.1 123.5 0.51 0.914 Error 30 7239.6 241.3 Total 71 120473.3 Postgraduate Certificate in Statistics Design and Analysis of Experiments

20 Lecture 6.120 © 2015 Michael Stuart Diagnostics Postgraduate Certificate in Statistics Design and Analysis of Experiments

21 Lecture 6.121 © 2015 Michael Stuart Same diagnostic, Different interpretation? Postgraduate Certificate in Statistics Design and Analysis of Experiments

22 Lecture 6.122 © 2015 Michael Stuart Check Interactions Postgraduate Certificate in Statistics Design and Analysis of Experiments

23 Lecture 6.123 © 2015 Michael Stuart Check Interactions Postgraduate Certificate in Statistics Design and Analysis of Experiments

24 Lecture 6.124 © 2015 Michael Stuart Check Interactions Postgraduate Certificate in Statistics Design and Analysis of Experiments

25 Lecture 6.125 © 2015 Michael Stuart Check Interactions Postgraduate Certificate in Statistics Design and Analysis of Experiments

26 Lecture 6.126 © 2015 Michael Stuart Interaction plots for Grassland experiment Treatments Postgraduate Certificate in Statistics Design and Analysis of Experiments

27 Lecture 6.127 © 2015 Michael Stuart Postgraduate Certificate in Statistics Design and Analysis of Experiments

28 Lecture 6.128 © 2015 Michael Stuart Design and Analysis of Experiments Lecture 6.1 1.Review of split unit experiments −Why split? −Why block? 2.Review of Laboratory 2 −Cambridge grassland experiment −Soup mix packet filling 3.An interesting interaction? 4.Course evaluation 5.Review of 2014 Annual Examination Postgraduate Certificate in Statistics Design and Analysis of Experiments

29 Lecture 6.129 © 2015 Michael Stuart Laboratory 2, Exercise 2: Soup mix packet filling machine Questions: What factors affect soup powder fill variation? How can fill variation be minimised? Potential factors A:Number of ports for adding oil,1 or 3, B:Mixer vessel temperature, ambient or cooled, C:Mixing time, 60 or 80 seconds, D:Batch weight, 1500 or 2000 lbs, E:Delay between mixing and packaging, 1 or 7 days. Response: Spread of weights of 5 sample packets Postgraduate Certificate in Statistics Design and Analysis of Experiments

30 Lecture 6.130 © 2015 Michael Stuart Minitab analysis Postgraduate Certificate in Statistics Design and Analysis of Experiments

31 Lecture 6.131 © 2015 Michael Stuart Minitab analysis Normal plot vs Pareto Principle vs Lenth? Postgraduate Certificate in Statistics Design and Analysis of Experiments

32 Lecture 6.132 © 2015 Michael Stuart Alias analysis Estimated Effects Term Effect Alias E -0.470 E + A*B*C*D B*E 0.405 B*E + A*C*D D*E -0.315 D*E + A*B*C E is aliased with or confounded with A*B*C*D Postgraduate Certificate in Statistics Design and Analysis of Experiments

33 Lecture 6.133 © 2015 Michael Stuart Graphical and numerical summaries Postgraduate Certificate in Statistics Design and Analysis of Experiments

34 Lecture 6.134 © 2015 Michael Stuart Best conditions Best conditions: Temp Low, Weight High, Delay High. Best conditions with Delay Low: Temp High, Weight Low. Postgraduate Certificate in Statistics Design and Analysis of Experiments

35 Lecture 6.135 © 2015 Michael Stuart Reduced model Fit model using active terms: B + D + E + BE + DE DE confirmed as active. Postgraduate Certificate in Statistics Design and Analysis of Experiments

36 Lecture 6.136 © 2015 Michael Stuart Diagnostics Postgraduate Certificate in Statistics Design and Analysis of Experiments

37 Lecture 6.137 © 2015 Michael Stuart Diagnostics Postgraduate Certificate in Statistics Design and Analysis of Experiments

38 Lecture 6.138 © 2015 Michael Stuart Delete Design point 5, iterate analysis Effect estimates similar Interaction patterns similar s = 0.15, df = 9 ( = 14 – 5 ) Mean SE Mean B*D*E - - - 1.700 0.153 + - - 1.205 0.108 - + - 1.975 0.108 + + - 1.225 0.108 - - + 0.975 0.108 + - + 1.360 0.108 - + + 0.690 0.108 + + + 0.940 0.108 0.69  2.26×0.15/√2 = 0.45 to 0.93 1.205  2.26×0.15/√2 = 0.965 to 1.445 Postgraduate Certificate in Statistics Design and Analysis of Experiments

39 Lecture 6.139 © 2015 Michael Stuart Design and Analysis of Experiments Lecture 6.1 1.Review of split unit experiments −Why split? −Why block? 2.Review of Laboratory 2 −Cambridge grassland experiment −Soup mix packet filling 3.An interesting interaction? 4.Course evaluation 5.Review of 2014 Annual Examination Postgraduate Certificate in Statistics Design and Analysis of Experiments

40 Lecture 6.140 © 2015 Michael Stuart Interaction between Factors Case study: Emotional Arousal Male and female subjects presented with four different visual stimuli, pictures of –an infant –a landscape –a male nude –a female nude Levels of subjects' emotional arousal were measured Arousal.xls Postgraduate Certificate in Statistics Design and Analysis of Experiments

41 Lecture 6.141 © 2015 Michael Stuart Interaction between Factors Case study: Emotional Arousal Infant Landsdcape Nude Female Nude Male 10 15 20 25 Male Pictures Infant Landsdcape Nude Female Nude Male 10 15 20 25 Female Pictures Levels of Arousal of Males and Females to Different Visual Stimuli Postgraduate Certificate in Statistics Design and Analysis of Experiments

42 Lecture 6.142 © 2015 Michael Stuart Interaction between Factors Case study: Emotional Arousal Postgraduate Certificate in Statistics Design and Analysis of Experiments

43 Lecture 6.143 © 2015 Michael Stuart Design and Analysis of Experiments Lecture 6.1 1.Review of split unit experiments −Why split? −Why block? 2.Review of Laboratory 2 −Cambridge grassland experiment −Soup mix packet filling 3.An interesting interaction? 4.Course evaluation 5.Review of 2014 Annual Examination Postgraduate Certificate in Statistics Design and Analysis of Experiments

44 Lecture 6.144 © 2015 Michael Stuart Design and Analysis of Experiments Lecture 6.1 1.Review of split unit experiments −Why split? −Why block? 2.Review of Laboratory 2 −Cambridge grassland experiment −Soup mix packet filling 3.An interesting interaction? 4.Course evaluation 5.Review of 2014 Annual Examination Postgraduate Certificate in Statistics Design and Analysis of Experiments

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