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15 Examples 273of this time rice plants were carefully extracted, the root system washed androot area determined for the tray using an image analysis system described byStevens et al. (1999). Two pairs of trays, each pair corresponding to a differentvariety, were included in each run. A new batch of bloodworm larvae was usedfor each run. A total of 44 varieties was investigated with three replicates of each.Unfortunately the variety concurrence within runs was less than optimal. Eightvarieties occurred with only one other variety, 22 with two other varieties andthe remaining 14 with three different varieties.In the next three sections we present an exhaustive analysis of these data usingequivalent univariate and multivariate techniques. It is convenient to use two datafiles one for each approach. The univariate data file consists of factors pair, run,variety, tmt, unit and variate rootwt. The factor unit labels the individualtrays, pair labels pairs of trays (to which varieties are allocated) and tmt is thetwo level bloodworm treatment factor (control/treated). The multivariate datafile consists of factors variety and run and variates for root weight of both thecontrol and exposed treatments (labelled yc and ye respectively).Preliminary analyses indicated variance heterogeneity so that subsequent analyseswere conducted on the square root scale. Figure 15.8 presents a plot of the treatedand the control root area (on the square root scale) for each variety. There isa strong dependence between the treated and control root area, which is notsurprising. The aim of the experiment was to determine the tolerance of varietiesto bloodworms and thence identify the most tolerant varieties. The definition oftolerance should allow for the fact that varieties differ in their inherent seedlingvigour (Figure 15.8). The original approach of the scientist was to regress thetreated root area against the control root area and define the index of vigour asthe residual from this regression. This approach is clearly inefficient since thereis error in both variables. We seek to determine an index of tolerance from thejoint analysis of treated and control root area.Standard analysisThe allocation of bloodworm treatments within varieties and varieties within runsdefines a nested block structure of the formrun/variety/tmt = run + run.variety + run.variety.tmt( = run + pair + pair.tmt )( = run + run.variety + units )