Download pdf guide - VSN International

68 5 Designs with several error termsExcept when comparing means with the same level(s) ofvariety 7.68d.f. 45The standard errors accompanying the tables of means also take account of the stratumwhere each treatment term was estimated. The Variety s.e.d. of7.08 = (2 × 601.3 / 24)is based on the residual mean square for Blocks.Wplots, while that for Nitrogen4.44 = (2 × 177.1 / 18)is based on that for Blocks.Wplots.Subplots. The Variety × Nitrogen table ismore interesting. There are two s.e.d.'s according to whether the two means to becompared are for the same variety. If they are, then the subplots from which the meansare calculated will all involve the same set of whole-plots, so any whole-plot variabilitywill cancel out, giving a smaller s.e.d. than for a pair of means involving differentvarieties.Split-plot designs do not only occur in field experiments, but they can occur in animaltrials (where, for example, the same diet may need to be fed to all the animals in a penbut other treatments may be applied to individual animals), or in industrial experiments(where different processes may require different sized batches of material), or even incookery experiments (see, for example, Cochran & Cox 1957, page 299). There can alsobe more than one treatment factor applied to the units of any stratum; to analyse theresults in GenStat, you simply need to specify the blocking factors, as above, and thenwhatever treatment structure is appropriate.GenStat specifies the structure of the design, and thus the different sources ofvariability (or strata) in the model, using the BLOCKSTRUCTURE directive (see Chapter9). For Figure 5.1, this wasBLOCKSTRUCTURE Blocks / Wplots / Subplotswhere the operator / indicates that a factor is nested within another factor. So we haveSubplots nested within Wplots (whole-plots) nested within Blocks, as required. Themodel formula expands to the list of model termsBlocks + Blocks.Wplots + Blocks.Wplots.Subplotswhich defines the strata to represent the variation between the blocks, between wholeplotswithin blocks, and between subplots within whole plots (within blocks) shown inthe analysis-of-variance table.The next section shows how you can define your own block structure in the menu, andspecify any stratified design.5.2 PracticalIn an experiment to study the effect of two meat-tenderizing chemicals, the two (back)legs were taken from four carcasses of beef and one leg was treated with chemical 1 andthe other with chemical 2. Three sections were then cut from each leg and allocated (atrandom) to three cooking temperatures, all 24 sections ( 4 carcasses × 2 legs × 3 sections) being cooked in separate ovens. The table below shows the force required to break astrip of meat taken from each of the cooked sections (the data are also in the fileMeat.gsh). Analyse the experiment.