September, 1951.]
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N.
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Some of the crossed lines were not old enough to provide complete perform-
ance data. There appear to be significant differences between the lambing
averages of the lines, but these differences are confounded with stations, since all
the lines are not represented at all the sub-stations. These differences, therefore,
defy interpretations.
There appear to be significant differences between second, third and fourth
year lambings within lines, as well as in the pooled total. To study this, the lamb-
ing records from the second to the seventh year of age are included. A ewe very
rarely lambs in this experiment in its first year and is culled out from the flock
after its seventh year of age. This is generally the productive period of a ewe and
so it is taken into consideration for this study.
The linear and curvilinear regressions of lambing averages on age were cal-
culated by the multiple covariance method as illustrated by Snedecor [1946]. This
analysis included all the lines, even though some of them were incomplete in their
performance up to the seventh year. The classification of the data was kept simple
by grouping them by lines and dams within lines to eliminate the differences due
to lines and dams. Both of the regressions were calculated from within dams within
lines by sums of squares and products.
Both of the regressions are highly significant, but the curvilinear regression is
significantly better fitted to the data than the linear regression. In Plate XIII, fig. A
is given a graph of the curvilinear regression (ct) without eliminating the difference
due to lines; (wd) after eliminating these differences and (ob) the observed lamb-
ing averages for the different ages at the time of lambing.
The curvilinear regression calculated from the data, excluding the incomplete
records of some of the lines are given in Plate I, fig. B. In this graph the regressions
and the observed lambing averages for the different ages show the same trend.
The regression from within dams within lines differences (wd) shows that the
lambing average rises with the increase in age up to the fifth year and then gradually
declines. At the seventh year it shows a rapid drop. In other words, the rate of
increase in lambing average gradually decreases as the age increases. The rapid
decline at the seventh year, or afterwards, is not of much significance, because of the
very low number of records.
Year effects. Since the lambings occur in the same season at one year intervals,
it is suspected that the age effect may be influenced by year effects. To eliminate
this effect, partial regressions of lambing average on age and year were calculated
from the same data.
Both the partial regressions (one, by x 1 .x 2 =.1405, the effect of age on lambing
average when year effect is removed and the other, byx 2 .x 1 =—.0698, the effect
of year when the effect of age is held constant) are highly significant. The reduc-
tions in the sums of squares of the lambing average when corrected for both year
and age effects are highly significant. The regressions indicate that if the environ-
mental effects from year to year were held constant there would be an average-
increase of .1405 lambs every year from the second year of age up to the fifth year
and then there would be decline. Similarly if the effects of age were to be held
constant there would be a reduction, according to these data, of 0698 lamb every