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7.6 Unbalanced designs with several treatment factors 93simply want to remove any day differences before assessing the treatments. The TreatmentStructure box contains a factorial model with treatment factors A, B and C.The commands that are generated by this setting of the menu use the GenStatregression facilities (via procedure AUNBALANCED) rather than the analysis-of-variancefacilities. So GenStat produces an accumulated analysis-of-variance, indicating the orderin which the terms were fitted. The term day is fitted first because this is a nuisanceterm, reflecting random variability which we want to eliminate before we assess thetreatments. The +A line then gives the (main) effect of A after eliminating day. The +Bline gives the main effect of B, eliminating day and A, and so on. Each line in the tablepresents the effect of a particular term, eliminating the terms in the lines above, butignoring the terms in the lines below. This is technically true also in the examplespresented in earlier chapters but there the designs were orthogonal and so the orderingof the treatment terms was unimportant. Here if we had specified C*A*B, the sums ofsquares for A, B and C would have been 1699.1, 429.4 and 1063.0 respectively, and therewould also have been changes to the sums of squares for the interactions. The resultswould have led to the same conclusions to those from the earlier order (namely that thereare main effects of A and C, and an A by C interaction), but in a design with a greaterdegree of non-orthogonality you would be well advised to investigate several orderings.Alternatively, the Options menufor the designs with UnbalancedTreatment Structure (Figure 7.11)contains a check box to allow you torequest screening tests.In the marginal test (the columnheaded “mtest” below) the term isadded to the simplest possiblemodel. So A.B would be added to amodel containing only the maineffects A and B. This assesses theeffect of the term ignoring as manyother terms as possible, and so itchecks to see if there is anyevidence for the term having aneffect.In the conditional test (thecolumn headed “ctest” below) theFigure 7.11term is added to the most complex possible model. So, A would be added to a modelcontaining B, C and B.C. This checks to see if the term has any effect that cannot beexplained by any other terms.Ideally (as here) the tests will both lead to the same conclusion. If not, the conclusionis that there is more than one plausible model for the data, but the design is toounbalanced to allow you to choose between them.Screening of terms in an unbalanced designVariate: Y