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112 8 REML analysis of unbalanced designs8.5 Analysis of variance by ANOVA, regression or REMLIn the earlier chapters of this Guide,you have seen that, if your design isbalanced you can produce an analysisif variance using the Analysis ofVariance menu (Figure 1.8), or youmay be able to use the One- and TwowayAnalysis of Variance menu (Figure1.14) if you have no more than twotreatment factors. GenStat will tellyou if the design is unbalanced.Figure 8.8Then, if it has only one error term you can use the Unbalanced ANOVA menu (Figure 7.9),or if it has several you can use the Linear Mixed Models menu (Figure 8.1). A smallcomplication is that you might want to use the Unbalanced ANOVA menu rather than theLinear Mixed Models menu, even when there several error terms, if the additional errorterms contain very little information about the treatments (and this was why we did notuse the Linear Mixed Models menu in Section 7.6).So you could define a set of rulesto decide how to analyse acomplicated design. However, youmight prefer GenStat to do this foryou and, in fact, it will do so if youuse the menu for Analysis of varianceby ANOVA, regression or REML. Figure8.9 shows the use of the menu toanalyse the production data inSection 7.6.Figure 8.9The Options menu (Figure 8.10)allows you to select only the types ofoutput that are available from all thepossible methods of analysis. Youcan also say how much information(i.e. efficiency) you are prepared tolose on any treatment term whendeciding to use whether to use theUnbalanced ANOVA menu (which usesregression) rather than the LinearMixed Models menu (which usesREML). The Information section willcontain details of the recommendedmethod, and the amount ofinformation that may have been lost.The output, below, confirms that it Figure 8.10was acceptable to use UnbalancedANOVA in Section 7.6: less than 1% of the information has been lost.