STUDIES ON THE DETERMINATION OF DIGESTIBILITY COEFFICIENTS  89

In this way, we can obtain the individual digestibility of two, three or more
feeds by conducting two, three or more trials depending on the number of feeds
used. Theoretically, such a procedure would be free from any blemishes, if at
the same time it satisfies the primary condition implicit in such an experiment,
viz., that the animal used behaved with mathematical uniformity. This, how-
ever, is next to impossible in actual practice. We have, therefore, to ascertain,
what should be the minimum number of animals compatible with a reliable
estimate of digestibility coefficient.

From the statistical standpoint, it is necessary to estimate the digestibility
coefficient independently from a number of animals and then test the agreement
between the results obtained. The closer the agreement, the greater the preci-
sion of individual estimates, hence the smaller the number of animals (i.e., repli-
cations) required for the test. But we must theoretically have, at least a dupli-
cation, if not more to obtain an estimate of the precision of a single observation.
This principle of replication must be kept in view to obtain an objective estimate
of the precision in all possible cases and it is exactly for this purpose that field
experiments in agriculture are always replicated. There are, however, instances
where the test has been confined to one single animal. In such cases, the calcula-
tion of digestibility on the basis of the above equation can be the only alternative,
despite its serious inherent limitations.

It will, however, be obvious that being based on the results of a single animal
(in other words single observation in the statistical sense), it will not be possible
to determine the extent of reliability of the digestibility coefficients. If, there-
fore, one or other sets of observations deviate appreciably from the normal condi-
tions, the estimates of digestibilities are bound to be correspondingly affected
without there being any means to detect their extent. Similarly, if the sets happen
to be normal ones, the results are expected to be as much satisfactory as is possible
within the range of the experiment. Such uncertainties in the calculation of
digestibilities should, however, be avoided, as far as possible, in scientific investi-
gations.

We should, therefore, have some definite knowledge as to what should be the
minimum number of replications necessary to attain a certain specified standard
of statistical accuracy. This will naturally imply a large number of individual
tests. We have a fairly large number of data from another experiment leading to
the paper on the estimation of digestibility coefficients [1934] and an analysis
of the same would serve as a proximate index of the extent of deviation of a single
observation.

It will, therefore, be necessary at this stage to give a short outline of the ex-
periment conducted with regard to the above paper. This experiment was based
on graphical representation and multiple regression equations with respect to two
feeds, viz., aman paddy straw and linseed cake, the latter being in doses of 1 lb.,