The visual impression was of increased growth at the orange orchard end of the experiment. If the trend is
gentle then a covariate of the distance from the left-hand end of the experiment may be adequate. If the
reduction in yield near the orange orchard is more sudden and severe then using the reciprocal of distance
may be appropriate (see Example 10.2 in Mead (1988))

43 Discarding or Adjusting Data

It is expected, as part of the general philosophy of OFR, that considerable variability of results will be
experienced, and there is an argument that, consequent on this expectation, all data should always be used
precisely so that this expected variability should be displayed. A counter argument is that sometimes
extreme observations or sets of data are patently not representative of the same population as the rest of the
data and this should be recognized and the analysis and interpretation amended accordingly.

There are different levels at which the discarding of data may be considered. Within a site there are
sometimes obvious causes for reduced yields on some plots. A very common example for maize is plots
having a markedly low number of plants. Although total plot yield compensates partially for lower density
through reduced competition there is usually a clear tend relating yield and plot density. This is an
appropriate situation for covariance analysis and adjustment with total discarding of plot data only in
extreme cases. In covariance the relationship between the principal variate (yield) and the concomitant
variate (density) is assessed for each treatment (allowing for block effects if this is necessary) and the
average trend is calculated. The treatment means are then adjusted to a common density level enabling
valid comparison of treatments unaffected by particular deviations of density. The progress of the
technique is demonstrated for four treatments each with two plots in Figure 1.

 Rep 1 Rep 2
 Yield (kg/ha) Density/plot Yield Density

 2.25 33 1.45 22
 1.90 30 2.15 40
 1.95 16 2.80 35
 2.55 32 2.85 39

The four slopes (in g/ha per plant/plot) are:

 0.8/11
 0.25/10
 0.85/19
 0.1/7

and the average slope is

 0.8 + 0.25 + 0.85 + 0.1 2 = 0.425
 11+10+19+7 47