First, just how much soil nitrogen will get to a plant depends on several
conditions, such as
( 1) how well the root system penetrates the soil (this in turn may depend
on the variety of corn, the supply of other nutrients, soil moisture
(2) the competition from weeds or other plants, and from soil bacteria,
for available nitrogen;
( 3) leaching of nitrogen from the soil by rain (this in turn will be influ-
enced by whether the field is flat or sloping, local rainfall variation,
speed of water run-off, and the chemical form of nitrogen in the soil
(nitrate-N, ammonium-N, etc.), and whether it was applied as artifi-
cial fertilizer or was residual from a previous N-fixing legume crop).
Second, when nitrogen has gotten to the plant, how it will influence yield
depends on how much has gone to the seed and how much to vegetative
growth. This in turn depends upon
( 1) when in the growth cycle the nitrogen is taken up by the plant;
(2) the variety of corn grown;
(3) the supply of other nutrients;
(4) the nature of the available nitrogen (nitrate-N, ammonium-N, etc.);
(5) meteorological factors such as temperature and moisture content.
Third, there may be other sources of fixed nitrogen available to the plant,
including any provided in precipitation (especially during or shortly after
Fourth, there may be further measurement errors in recording yield not
only through loss at harvesting, but due to bird or storm damage, or discrep-
ancies due to weighing or harvesting part of the crop at a nonoptimum time
(e.g., at different stages of ripeness).
Clearly, then, a true straight-line relationship between soil nitrogen and
corn yield is an unattainable ideal. That is not to say that we should not
seek such a relationship or determine whether it is a good approximation in
certain circumstances. It would seem that to get a really good model we need
either to bring more variables into our equation or control certain variables.
There is inevitably a practical compromise between what is experimentally
feasible and how complex a model we can fit or analyse.
That statisticians are moving toward more complex models is clear from
the programme for this meeting. In dealing with historical aspects the treat-
ment has been confined largely to single (often bivariate) relationships. Fu-
ture research promises to be more multivariate and often nonlinear; such
models are increasingly common in the literature.
My choice of Fuller's example for illustration is in no way a criticism of
his analysis of the data. I know from discussions I have had with him that
he is as conscious as I of the limitations in modelling imposed by the nature
of data and experimental factors. I chose this example because it provides