3. Statistics
The defecation data in the three experiments were amalgamated for analysis. The data was available as mob-day totals, summarised as the numbers of defecations in the stream, the riparian zone (bank plus stream) and the whole of the field. There were too few defecation data to split into the nominal areas of the field (top, middle and bottom).
Data were initially examined as potentially Poisson-distributed counts using the GLMM procedure in the Genstat statistical package to determine the error structure required to model the correlation’s inherent to repeated measures data.
The presence of error strata for mob, day and field clustering were tested for, allowing for fixed effects arising from a general difference between the three experimental sets of data. The fixed effects were season (with and without distinction between the two summer periods), day of grazing within grazing-period (as a reflection of changing pasture availability), absence of a drinking trough in fields, presence of a shade structure in the riparian zone, and forage treatment in the riparian zone. The latter two effects arose only in Experiment 3 and the trough effect only arose in Experiments 1 and 2. The fixed effects were tested both in models that restricted their effect to the relevant experimental data sets and as overall comparisons, as the fixed effects model was reduced by omitting the negligible effects. Terms were nominally rejected at the p > 0.05 level, but in fact p-values were generally much higher for most fixed effect tests.
Both "in water" and total defecations in the riparian area led to the conclusion that variation arose solely from random mob-to-mob differences with residual Poisson variation. Whole field numbers on the other hand showed an overall average difference between summer-autumn and winter-spring periods with no error structure, but a residual greatly in excess of that expected from Poisson variation. Analysis of data was therefore completed by confirming fixed effects in Gamma error regression models to the mob per cow per day averages for "in water", total data for the riparian zone and per cow per day individual observations for the whole field data respectively. Gamma variation was confirmed by testing the fit of various alternatives for error distribution.
The percentage of whole field defecations observed "in the water" or in the riparian zone were also analysed. This led to a model comprising between mob average variation with a binomially distributed day-to-day residual. Mob averages were very well fitted by Beta distributions.
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