Download pdf guide - VSN International

More documents

Recommendations

Info

26 2 Blocking structuresNow we repeat the analysis,checking the Blocks box to showthat there is a block factor, andentering specifying Litter in thebox alongside.Figure 2.3Analysis of varianceVariate: GainSource of variation d.f. s.s. m.s. v.r. F pr.Litter stratum 7 6099.47 871.35 21.44Litter.*Units* stratumDiet 4 346.87 86.72 2.13 0.103Residual 28 1137.73 40.63Total 39 7584.07Tables of meansVariate: GainGrand mean 65.3Diet A B C D E62.6 65.4 64.2 63.3 70.9Standard errors of differences of meansTable Dietrep. 8d.f. 28s.e.d. 3.19The analysis of variance now has an additional line "Litter stratum" that records thevariation between the complete litters of rats. (Diets are now estimated in theLitter.*Units* stratum, which represents the variation within litters.) The betweenlittersum of squares (6099.47) has been subtracted from the original residual sum of
2.2 Randomized block designs 27squares. So the residual sum of squares is now 7237.2 6099.47 = 1137.73. As a result,the residual mean square has decreased from 206.8 to 40.63, and the standard error fordifferences between the diet means has decreased from 7.19 to 3.19. This increase inprecision means that we have a better chance of detecting differences between the diets,In fact, as you can see, the probability for the variance ratio of diet has decreased from0.794 to 0.103 (still not significant, but getting closer!). You can see that the precisionhas improved from the fact that the variance ratio for the Litter stratum is greater thanone this indicates that the degrees of freedom that we have taken out of the originalresidual have more variability than those that are left.Informally, blocking can be seen as a sort of insurance against large variation betweengroups of units which could increase your estimate of background variability, making itharder to detect treatment differences. In general, you don't have to know for certain thatdifferences between groups will exist before you use blocks. If you suspect that certaingroups of units may differ from each other, you should use those groups as a blockingfactor. If the differences do appear, your estimated treatment effects will be more precisethan if you had not used the blocks; if they don't, then generally you will be no worse off.Blocks most commonly correspond to position: units situated together will be subject tothe same conditions and are therefore put into the same blocks.You should also use your blocks to guard against differences introduced by theexperimental procedure or husbandry of a field experiment. For example, you shouldmake sure that the harvesting of a field experiment is done by blocks so that anydifferences due to harvesting time (or different machines) are accounted for bydifferences between blocks. Similarly, if subjective data (e.g disease scores) are to becollected by several observers, you should make sure that each observer collects datafrom a whole block so that differences between observers are accounted for bydifferences between blocks.You will be at a disadvantage from using blocking only if you have got the blockswrong, so that units within blocks are dissimilar. For example, if the field experimentdiscussed above had used blocks running down the hill rather than across the hill, unitswithin blocks could not be considered identical. For this reason, care should be takenwhen forming blocks. If no obvious groups of similar units exist, a completelyrandomized design may be the best solution.To generate a randomized-block design, you must first decide how many treatmentsare to be used in the experiment and then how many blocks, or replicates, are to be usedfor each treatment. Sometimes the size of your blocks may restrict the number oftreatments you can test. You must use enough replicates to give a reasonable number ofresidual degrees of freedom, this ensures that you have a good estimate of the randomerror and your estimates of treatment effects will be more precise as replication increases.As a general rule, between 10 to 20 residual degrees of freedom is adequate.Once you have decided on the number of blocks and treatments to be used, you mustrandomize the experiment. This means that for each block separately, you must generatea random ordering of the treatments to be applied to the units within each block. Thisrandomization within blocks guards against any unsuspected sources of bias in theexperiment. For example, for a medical experiment, it means that an experimenter couldnot introduce bias by giving the placebo treatment to the subjects who appeared to beleast sick. If an unsuspected fertility trend ran across the hill in the field experiment weanalysed earlier, then an unrandomized experiment with all blocks in order A, B, C, D
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 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 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 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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?