THE USE O F STATISTICS IN. PHYTOSOCIOLOOY
63
which we ourselves believe to be the more important reason for the use
of statistical techniques in much phytosociological and ecological work.
Some difficulties arise in the definition of “efficiency” in the sense
we intend it here. In the modern, restricted, statistical literature, the
efficiency of a statistic is related to the precision of an estimate from a
given size of sample in an unknown population. In the present context,
however, this definition is largely irrelevant except in so far as similar
underlying concepts are involved. For present purposes, we shall define
the term as the optimization of the amount of information extracted
from a given situation for a given quantity of work; and this includes
the wider concepts of time and effort spent in data-collecting, in processing the data, and in interpreting the results.
As regards efficiency of analytical methods, the most relevant property
of most phytosociological (and ecological) data is its complexity. With
modern computer facilities, however, a number of quite elaborate nonprobabilistic techniques appropriate to complex data are now coming
within reach; and the saving of personal time and effort by using
mechanical methods of analysis is often so considerable that no modern
ecologist can afford to ignore the possibilities which exist. At the same
time, computer-time costs money, and any statistical technique proposed should be rigorously scrutinized on the efficiency criterion suggested before it is adopted. For instance, it is often necessary tobalance
the efficiency of a given parameter for a given estimation against a
disproportionate increase in total computing time ; and methods which
give the maximum information are not necessarily to be preferred
against more approximate methods which are faster to operate.
Similarly, the method of data-collection should be pruned as far as
possible consistent with an acceptable reduction in information-content
of the samples to be analysed: it is often more efficient to work with a
larger number of samples of low individual information-content than
with a smaller number of much more elaborate and time-consuming
records.
In any use of statistical techniques as investigational tools, therefore,
there are three basic requirements to be met. First, the tool must be
appropriate to the material to be worked, i.e. the nature and form of
the data, and the scale of the problem, must be considered in selecting
the most efficient method; secondly, the tool itself must be of sound
construction (i.e. the underlying mathematics must be sound), and any
area of weakness must be clearly understood so that an undue strain
is not imposed; and thirdly, the work to be done must itself be clearly
defined, i.e. the questions to be asked must be precisely formulated, so
that a misleading or nonsensical answer is not inadvertently obtained.
Although such general requirements are obviously not unique to
63
which we ourselves believe to be the more important reason for the use
of statistical techniques in much phytosociological and ecological work.
Some difficulties arise in the definition of “efficiency” in the sense
we intend it here. In the modern, restricted, statistical literature, the
efficiency of a statistic is related to the precision of an estimate from a
given size of sample in an unknown population. In the present context,
however, this definition is largely irrelevant except in so far as similar
underlying concepts are involved. For present purposes, we shall define
the term as the optimization of the amount of information extracted
from a given situation for a given quantity of work; and this includes
the wider concepts of time and effort spent in data-collecting, in processing the data, and in interpreting the results.
As regards efficiency of analytical methods, the most relevant property
of most phytosociological (and ecological) data is its complexity. With
modern computer facilities, however, a number of quite elaborate nonprobabilistic techniques appropriate to complex data are now coming
within reach; and the saving of personal time and effort by using
mechanical methods of analysis is often so considerable that no modern
ecologist can afford to ignore the possibilities which exist. At the same
time, computer-time costs money, and any statistical technique proposed should be rigorously scrutinized on the efficiency criterion suggested before it is adopted. For instance, it is often necessary tobalance
the efficiency of a given parameter for a given estimation against a
disproportionate increase in total computing time ; and methods which
give the maximum information are not necessarily to be preferred
against more approximate methods which are faster to operate.
Similarly, the method of data-collection should be pruned as far as
possible consistent with an acceptable reduction in information-content
of the samples to be analysed: it is often more efficient to work with a
larger number of samples of low individual information-content than
with a smaller number of much more elaborate and time-consuming
records.
In any use of statistical techniques as investigational tools, therefore,
there are three basic requirements to be met. First, the tool must be
appropriate to the material to be worked, i.e. the nature and form of
the data, and the scale of the problem, must be considered in selecting
the most efficient method; secondly, the tool itself must be of sound
construction (i.e. the underlying mathematics must be sound), and any
area of weakness must be clearly understood so that an undue strain
is not imposed; and thirdly, the work to be done must itself be clearly
defined, i.e. the questions to be asked must be precisely formulated, so
that a misleading or nonsensical answer is not inadvertently obtained.
Although such general requirements are obviously not unique to