Slide 1 Chapter 13: ANOVA for 2-way classifications (2 of 2) Fixed and Random factors, Model I, Model II, and Model III (mixed model) ANOVA Chapter 14: Unreplicated Factorial & Nested Designs Slide 2 HW 15 due Weds 5/6/09 10 am Slide 3 Case 13.2 Pygmalion Effect Page 1 of 33
Slide 4 Pygmalion effect Slide 5 Pygmalion Effect Slide 6 Pygmalion results Page 2 of 33
Slide 7 Strategies for factorial analysis Slide 8 Additive and non-additive models Slide 9 Page 3 of 33
Slide 10 ì{score Pygm,company}=Pyg+comp Slide 11 Slide 12 Page 4 of 33
Slide 13 Visual binning to examine residuals Slide 14 ì{score Pygm,company} = Pyg+company+Pyg x company Slide 15 Page 5 of 33
Slide 16 Extra sum of squares F test Slide 17 Slide 18 Page 6 of 33
Slide 19 Unbalanced designs & effect sizes Slide 20 Exact Test for Pygamalion Effect Slide 21 Nonadditivities & interactions Page 7 of 33
Slide 22 Fixed vs. Random Factors Slide 23 Fixed vs. Random factors Slide 24 Fixed vs. Random factors Page 8 of 33
Slide 25 Fixed Factor (Model I) Factorial ANOVA Slide 26 Random Factor (Model II) Factorial ANOVA Slide 27 Model II & Mixed Model (Model III) Factorial ANOVAs Page 9 of 33
Slide 28 SPSS mixed effects ANOVA Slide 29 When should a factor be regarded as random instead of fixed? Slide 30 13.2 Companies as a random effect Page 10 of 33
Slide 31 Effect size of Pygmalion treatment Slide 32 Conclusions to Case 13.2 Slide 33 Conclusion from Chapter 13 Page 11 of 33
Slide 34 Chapter 14: Multifactor studies without replication Slide 35 Strategies for analyzing tables with one observation per cell Slide 36 Case 14.01 Page 12 of 33
Slide 37 Statistical results, Case 14.1 Slide 38 Coded boxplot Slide 39 Table of estimated means Page 13 of 33
Slide 40 Horn-shaped residuals Slide 41 Log-transformed learning times Slide 42 No replication: no interaction test Page 14 of 33
Slide 43 Acquisition time as a blocked ANOVA, chimp as a blocking variable Slide 44 Log-transformation & Interaction Slide 45 Tukey one degree of freedom test Page 15 of 33
Slide 46 Matlab s Tukey additivity test Slide 47 Slide 48 Summary of statistical findings Page 16 of 33
Slide 49 Case 14.2 Slide 50 Case 14.02 Slide 51 Summary of statistical findings Page 17 of 33
Slide 52 Summary of statistical findings Slide 53 Strategies for analyzing tables with one observation per cell Slide 54 Residual plots to assess model misspecification Page 18 of 33
Slide 55 Log (Yield) vs. Ozone Slide 56 Scatterplots of expected effects Slide 57 Williams cultivar Page 19 of 33
Slide 58 ANOVA tables for Soybean yield Slide 59 Conclusion about main effects Slide 60 Final results for Soybean yield Page 20 of 33
Slide 61 Is there really no interaction? Slide 62 Nested (=hierarchical) ANOVA Slide 63 Pseudoreplication= model misspecification Page 21 of 33
Slide 64 Nested design (Experimental units [buckets] nested within treatment) Slide 65 Nested (hierarchical) ANOVA Slide 66 Nested ANOVA, with Expt Units random Page 22 of 33
Slide 67 How to perform Nested ANOVA Slide 68 How to perform a Nested ANOVA Slide 69 How to perform a Nested ANOVA Page 23 of 33
Slide 70 Effects of predation on Hobsonia Slide 71 Nested ANOVA Slide 72 Mixed model nested ANOVA equivalent to ANOVA on the means Page 24 of 33
Slide 73 Blocked ANOVA removes East vs. West variance Slide 74 Nesting vs. Blocked ANOVA Slide 75 Is there a gender difference in learning? Page 25 of 33
Slide 76 Chimp Nested ANOVA Slide 77 Test gender effect over among chimp within gender mean square Slide 78 Chimps should be regarded as a fixed factor, not random Page 26 of 33
Slide 79 Nested ANOVA with chimp as a fixed effect is identical to a linear contrast on sex (specified a priori) Slide 80 Results of testing gender effect using linear contrast: chimp ½ ½ -1/2-1/2 Slide 81 Case Study 5.2 redux: District judges Random or Fixed Page 27 of 33
Slide 82 Mixed Model Nested ANOVA Slide 83 Nested vs. Crossed Factors Slide 84 Nested vs. Crossed Page 28 of 33
Slide 85 Slide 86 Are experimental units fixed or random factors? Slide 87 Two-factor Fixed Effects model Page 29 of 33
Slide 88 Slide 89 This example: Model I nested ANOVA Slide 90 Instructors as fixed factors Page 30 of 33
Slide 91 Instructors as random factors Slide 92 If instructors treated as a random factor, there is no effect of city Slide 93 Case Study 14.2 was based on a Split-plot design. These designs are common in agriculture and industrial applications, but less common in environmental Science. The following slides present an example of a split-plot design to assess the effects of trawling on benthic communities Page 31 of 33
Slide 94 Split-plot designs Slide 95 THE EFFECTS OF TRAWL GEAR ON SOFT BOTTOM HABITAT Slide 96 Testing for a trawl effect Page 32 of 33
Slide 97 Lessons to be learned from the trawl study s design Page 33 of 33