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36 3 Treatment structureFigure 3.3 Figure 3.4This affects the way the conclusions of the experiment are described in a resulting paperor report: if there was an interaction you might need to write, for example "for low andhigh levels of sulphur, the yields improved linearly with increasing levels of nitrogen,whereas for sulphur at 10kg they seemed to level off above 180kg of nitrogen". If therewas no interaction this might become "application of 10kg sulphur improved yields butthere seemed to be no further benefit from higher amounts; yields increased linearly withnitrogen, irrespective of the amount of sulphur". It also affects the tables or figures thatshould be presented. If there is an interaction, you will need to present the two-way tableof means (nitrogen × sulphur); that is, you will need to present their effects jointly. Ifthere is no interaction, you can simply present the one-way table for each of the maineffects that is needed in the model.A plot like Figure 3.3 may help to explain the interaction, or even suggest a way ofmodelling it. We shall explore these ideas further in the next section.3.2 Fitting contrastsSometimes there may becomparisons between the levels of atreatment factor that you areparticularly keen to assess. Forexample, you might have had aninitial suspicion that there would belittle difference between the 180 and230 levels of nitrogen in theprevious section, but similar (andlarger) differences between 0 andFigure 3.5180, and between 0 and 230. Youmight then want to fit a single mean for the 180 and 230 levels of nitrogen, and assess thecontrast between this value and the mean for level 0.