J. C. BERRY AND J. L. LUSH 277
WHY NOT THE LOW?
To demonstrate more clearly how subsequent selection of a record because
of its size affects the correlation coefficient, the lowest of the five records was
correlated with the average of the remaining four and also with the average
of all five. In our data the low record was less variable (σ = 82) than the
high ( σ= 96) and hence had less influence in determining the variation of the
averages of five. For that reason alone, the low might be expected to be
somewhat less closely correlated with the average than was the highest record.
Moreover, the forces which tend to make the highest record large and those
which tend to make the lowest record small may be different enough that the
corresponding covariances may not be entirely comparable. For example,
some of the low records may have been made under circumstances definitely
known to have been abnormal but not specific enough that it would be prac
tical for us (or for the breed association) to undertake any corrections for
these circumstances. (Although this is plausible, it seems not to have been
important, because the low records averaged only 102 pounds below the
average of all five, whereas the high records averaged 98 pounds above.
Therefore the distribution seems to have been nearly symmetrical). While
the coefficients for the lowest record (.79 and .70 in Table I) are not as large
as those for the highest record, yet they are much larger than correlations
involving unselected records. The reasons are the same in principle as those
discussed in connexion with Figures 1 and 2.
Before passing from this consideration of the lowest record some com
ment might be ventured relative to the practical considerations involved.
Dairymen frequently raise objections to including all records of production
in averages because they feel that some lactations are abnormal. Such objec
tions are usually raised, however, after the cow has completed (or nearly
completed) a low record. That is, it is difficult (in practice usually impos
sible) to know whether the circumstances were judged abnormal solely be
cause of them or largely because it was seen that the record was going to be
low. Theoretically, the omission of records known to have been made under
definitely abnormal conditions for which adequate corrections cannot be made
would, we think, enhance the value of the resultant averages. However,
practical difficulties connected with deciding what constitutes grounds for
omission, and with making sure that the size of the record itself does not
influence the decision to use it or omit it, render the advisability of omitting
any records from lifetime averages problematical. Certainly the reasons for
such omission would have to be so specific and important that the decision
in each case would be automatic. For example, in Denmark only those
records made in years when the cow aborted or when she had foot-and-mouth
disease are omitted from her average.
PREDICTION OF FUTURE RECORDS OF THE SAME COW
The utility of the high record, as compared with that of unselected records
may be tested in the following way freed (we think) of those statistical
fallacies which beset of the correlation of the high record with the others from
which it was selected. The highest, lowest and medium records among the