Download pdf guide - VSN International

More documents

Recommendations

Info

8 1 From t-test to one-way anova1.2 PracticalSeven plants of wheat grown in pots and given nofertilizer treatment yield 8.4, 4.5, 7.8, 6.1, 4.7, 11.2 and9.6g dry weight of seed. A further eight plants from thesame source are grown in similar conditions but givena fertilizer treatment. These plants yield 11.6, 7.5, 10.4,8.4, 13.0, 9.6, 13.2 and 9.9g dry weight respectively.The data are held in file Pots.gsh as two columns: thefirst holds the seed weights (variate seed) and thesecond holds factor treat indicating whether or notthere was any fertilizer (control/fertilizer).Read the data into Genstat, then look to see whetherthe fertilizer has an effect on seed production bycarrying out a two-sample t-test using the T-Test menu.Figure 1.61.3 One-way analysis of varianceAnother way of representing thesituation, is that we have a linearmodely ij = ì + a i + åijwhere each observation isrepresented by its mean m i(which we have chosen to writeas ì + a i ) plus a residual åijwhich represents the randomvariation in the situation.For our example, it representsthe data as follows:
standard 23 2219 2120 1718 20new 24 2122 2025 2624 221.3 One-way analysis of variance 9= 21.5 + standard 1.5 + standard 3 21 10 3-2 0new 1.5 new 1 21 32 31 1y ì a å^^ij i ijThe residual variation can arise from many different causes, for example:• the units may not be absolutely identical (and we shall discuss later how units shouldbe allocated to treatments to take account of this),• they may then experience slightly different conditions during the experiment,• there may be measurement errors,• they may be being dealt with by different people during the experiment.The form of the model suggests another approach. If we were to assume that thetreatments are both identical, then their effects a 1 and a 2 would be zero. Our model wouldsimply bey = ì + åijijand we would estimate the grand mean ì by the average of all the data values: that isOne way of measuring how well this model fits is to take the sum of squares of theresiduals from this model (that is, to add up the squares of our estimates of the randomvariation on each observation for this model).This has n 1 + n 2 1 degrees of freedom as we have fitted just one parameter, ì.Now compare this with the full model above, in which the treatments are assumed tohave different effects: we can estimate a i by the mean of the observations that receivedtreatment i, minus the overall mean, that isand the residual sum of squares is
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 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 18 and 19: 14 1 From t-test to one-way anovaYo
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
Page 66 and 67:
62 4 Checking the assumptionsTotal
Page 68 and 69:
64 4 Checking the assumptionsMessag
Page 70 and 71:
66 5 Designs with several error ter
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
74 6 Design and sample size6.1 Desi
Page 80 and 81:
76 6 Design and sample sizeClicking
Page 82 and 83:
78 6 Design and sample sizeFigure 6
Page 84 and 85:
80 6 Design and sample sizeFigure 6
Page 86 and 87:
82 7 Balance and non-orthogonality7
Page 88 and 89:
84 7 Balance and non-orthogonalityA
Page 90 and 91:
86 7 Balance and non-orthogonalityT
Page 92 and 93:
88 7 Balance and non-orthogonalityF
Page 94 and 95:
90 7 Balance and non-orthogonalityf
Page 96 and 97:
92 7 Balance and non-orthogonality7
Page 98 and 99:
94 7 Balance and non-orthogonalityM
Page 100 and 101:
96 7 Balance and non-orthogonalityM
Page 102 and 103:
8 REML analysis of unbalanced desig
Page 104 and 105:
100 8 REML analysis of unbalanced d
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
9 Commands for analysis of variance
Page 120 and 121:
116 9 Commands for analysis of vari
Page 122 and 123:
118 9 Commands for analysis of vari
Page 124 and 125:
IndexA2DISPLAY procedure 117A2WAY p
Page 126:
122 IndexTransformation 56logarithm
show all

Download pdf guide - VSN International

Create successful ePaper yourself

Delete template?

Save as template?