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12 1 From t-test to one-way anovaAlternatively, we can useGenStat. The Analysis of Variancesection of the Stats menu on themenu bar (Figure 1.7) offers twopossibilities. One-way analysis ofvariance is easiest with the One- andtwo-way Analysis of variance menu(Figure 1.8). Later in the Course, weFigure 1.7will introduce the general Analysis ofVariance menu, which accesses the full power of GenSat's analysis of variance facilities.We select One-way as the Design,enter the name of the Y-variate(yield) and of the factor definingthe Treatments (method), and thenclick on Run.The output from the analysis iscontrolled by the ANOVA Optionsmenu (Figure 1.9), obtained byclicking on the Options button onthe One- and two-way Analysis ofvariance menu.With the analysis-of-variancetable, we usually also present tablesof means with associated standarderrors or (more usefully) standarderrors for differences between pairsof means (s.e.d's): for two meanswith replication n and n ,1 2Figure 1.8Figure 1.9s.e.d. = { (residual-mean-square) × (1/n 1 + 1/n 2) }= { (residual-mean-square) × (n 1 + n 2) / (n 1 × n 2) }You may recognise this as the denominator of the t-statistic from Section 1.1. In factdifferences between means from analysis of variance, divided by their s.e.d., also followt distributions (with degrees of freedom given by the residual d.f.).GenStat can also produce least significant differences. These are s.e.d.'s multiplied bythe relevant t value, allowing a direct comparison with the difference between the means.