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14 1 From t-test to one-way anovaYou can click on the Means Plotsbutton to open the ANOVA MeansPlots menu. This allows you tochoose how you want to plot themeans, and how you want torepresent their standard errors. InFigure 1.11 we have chosen to plotpoints for the means, with a bar toshow the s.e.d. (see Figure 1.12).You would plot lines if thetreatments represented differentamounts of some quantity such as a Figure 1.11fertilizer, a drug or a dietarysupplement. Plotting the data values (as well as the means) can provide a visualconfirmation of the significance (or non-significance) of the treatment effects reportedin the analysis-of-variance table. The final possibility is to plot the means as a bar chart.1.4 PracticalFigure 1.12Do a one-way analysis of variance for the data in Pots.gsh and compare the results withthose from the t-test. Plot the means, and also plot the data values. Does the plot with thedata values confirm what you have found in the analysis of variance?
1.5 One-way analysis of variance with several treatments1.5 One-way analysis of variance with several treatmentsDiet WeightThe advantages of analysis of variancebecome clearer when there are more thana 81.5 80.7 80.3 79.8two treatments.Spreadsheet file Rat.gsh contains datab 81.6 81.9 80.4 80.4 from an experiment to study the effect ofc 83.5 81.6 82.2 81.3a dietary supplement on the gain in weightof animals. There were five differentd 82.4 83.1 82.8 81.8 treatments (representing different amountse 83.2 82.8 82.1 82.1of the supplement) and twenty animalswere allocated at random, four to eachtreatment.The data can again be analysed using the One- and two-way Analysis of variance menu.Analysis of varianceVariate: weightSource of variation d.f. s.s. m.s. v.r. F pr.diet 4 12.7930 3.1982 6.32 0.003Residual 15 7.5925 0.5062Total 19 20.3855Tables of meansVariate: weightGrand mean 81.76diet a b c d e80.58 81.08 82.10 82.53 82.55Standard errors of differences of meansTable dietrep. 4d.f. 15s.e.d. 0.503Least significant differences of means (5% level)Table dietrep. 4d.f. 15l.s.d. 1.072
Page 1 and 2: Anova and Design
Page 4 and 5: ContentsIntroduction 11 From t-test
Page 6 and 7: 1 From t-test to one-way anovaIn th
Page 8 and 9: 4 1 From t-test to one-way anovaIf
Page 10 and 11: 6 1 From t-test to one-way anovaWe
Page 12 and 13: 8 1 From t-test to one-way anova1.2
Page 14 and 15: 10 1 From t-test to one-way anovawi
Page 16 and 17: 12 1 From t-test to one-way anovaAl
Page 20 and 21: 16 1 From t-test to one-way anovaFi
Page 22 and 23: 18 1 From t-test to one-way anovaTa
Page 24 and 25: 20 1 From t-test to one-way anovaTh
Page 26 and 27: 2 Blocking structuresThe blocking s
Page 28 and 29: 24 2 Blocking structuresBlock 1D4.6
Page 30 and 31: 26 2 Blocking structuresNow we repe
Page 32 and 33: 28 2 Blocking structureswould give
Page 34 and 35: 30 2 Blocking structuresAnalysis of
Page 36 and 37: 3 Treatment structureSo far we have
Page 38 and 39: 34 3 Treatment structureTables of m
Page 40 and 41: 36 3 Treatment structureFigure 3.3
Page 42 and 43: 38 3 Treatment structureThere is a
Page 44 and 45: 40 3 Treatment structureblock.*Unit
Page 46 and 47: 42 3 Treatment structureTables of c
Page 48 and 49: 44 3 Treatment structureN * Swas us
Page 50 and 51: 46 3 Treatment structureFumigant Am
Page 52 and 53: 48 3 Treatment structureFumigated S
Page 54 and 55: 50 3 Treatment structureCovariate 1
Page 56 and 57: 4 Checking the assumptionsIn this c
Page 58 and 59: 54 4 Checking the assumptions4.2 No
Page 60 and 61: 56 4 Checking the assumptions4.5 Tr
Page 62 and 63: 58 4 Checking the assumptionsFigure
Page 64 and 65: 60 4 Checking the assumptionsThe pr
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64 4 Checking the assumptionsMessag
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66 5 Designs with several error ter
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74 6 Design and sample size6.1 Desi
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76 6 Design and sample sizeClicking
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78 6 Design and sample sizeFigure 6
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80 6 Design and sample sizeFigure 6
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82 7 Balance and non-orthogonality7
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84 7 Balance and non-orthogonalityA
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86 7 Balance and non-orthogonalityT
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88 7 Balance and non-orthogonalityF
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90 7 Balance and non-orthogonalityf
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92 7 Balance and non-orthogonality7
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94 7 Balance and non-orthogonalityM
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96 7 Balance and non-orthogonalityM
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8 REML analysis of unbalanced desig
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100 8 REML analysis of unbalanced d
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9 Commands for analysis of variance
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116 9 Commands for analysis of vari
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118 9 Commands for analysis of vari
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IndexA2DISPLAY procedure 117A2WAY p
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122 IndexTransformation 56logarithm
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