6 Florida Agricultural Experiment Stations
the breeding program. Records included breeding, weight
changes and productivity of all cattle. Calves were weighed
at birth and all animals were weighed at 28-day intervals. The
data included records on 673 calves obtained from 254 cows
from this herd.
Weaning weights of calves were adjusted to a mean weaning
age of 180 days, based on a regression coefficient of 1.5 pounds
per day determined from the data. Approximate correction for
sex difference was made by adding 28.3 pounds to the weaning
weight of heifers. This difference in weight due to sex was
obtained from within sub-group averages and was in close agree-
ment with results reported by Koger and Knox (14), who found
a sex difference of 30 pounds in their data. Since the influence
of age of dam was of small magnitude in these data, no cor-
rection was made for this factor. The remaining sources of vari-
ability involved year-to-year effects, sire effects, seasonal effects
and breeding of dam.
The mathematical model assumed for the analysis was:
YljkU = m + yi + sj + tk + di + eijklm;
where:
Yijim is the weight of the ijklmth calf;
m is the general mean;
Yi is the ith year effect;
sj is the effect of the jth sire;
tk is the effect of the kth time;
di is the effect of the lth breeding of dam;
eijkim is the error for the mth individual in the ijklth group.
Each observation was assumed to be the sum of the influences
of effects of the variables as follows: Weaning weight = general
mean + year differences + sire differences + time of calving +
breeding of dam + error. This linear combination of effects is
similar to that used by Koch (12).
The least squares solution for disproportionate frequency dis-
tribution was employed for these data. Based on the mathe-
matical model given above, 21 simultaneous equations evolved
from these data. The method of analysis employed was the
Abbreviated Doolittle method from which estimates of treat-
ment effects were obtained and analysis of variance for the
treatment effects were determined (Anderson and Bancroft,
1952) (1).