ANALYSIS OF WEIGHT RECORDS OF ETAH GOATS
By C. K. DILWALI, B.Sc. (HONS.), M.A., Research Scholar in Statistics, Imperial Council of
Agricultural Research, New Delhi
(Received for publication on 1 April 1942)
(With two text-flgures)
THE Etah, farm started goat breeding work in
1932 with Barbari and Jumna Pari breeds. They
started with, a foundation stock of 36 Barbari
goats, nine kids and three bucks. Six more goats
were purchased later. The three purchased bucks
were given the register-numbers 48M, 49M and
50M. and a fourth buck purchased later was num-
bered 631M. Some of the foundation stock was
also mated to the male progeny of 48M and 49M.
The daughters of the foundation stock we shall
hereafter call, for convenience, as the first genera-
tion, the daughters of these as the second genera-
tion and so on. Jumna Pari stock purchased in
1932 was 47 goats and four bucks. Later addition
brought up the purchased number of Jumna Pari
goats to 104.
Each kid was weighed when born correct to 4 oz.
as the smallest unit. Every month the kids were
weighed on the 15th and the 30th, till, the kids
became one year old. These weight records are
available for both the breeds from 1934 to 1940.
The object of the paper is to analyse the weight
records for the following points :
(i) To compare the breeds and sexes regarding
the mean live weight (m.l.w.) and growth-rate.
(ii) To find the best season for breeding goats.
(iii) To find out if the breeding policy of the
farm has resultad in any improvement in the
m. 1. w. and growth-rate.
(iv) To find, out if m.l.w. and growth-rate are
correlated with the initial weight.
Statistical analysis. The very first step was to
evolve a satisfactory growth-curve, i.e. a curve
showing growth at various intervals. For this
six males and six females of each breed were select-
ed at random. Kidding time is shown on each
curve. Graphs of growth-curves for these were
drawn representing time along the horizontal axis,
with 15 days as unit, and weight along the vertical
axis with one pound as unit. A few of these curves
are reproduced here in Figs. 1 and 2. The curves
showed two turnings (called the points of inflexion)
with concavity of one of these turnings towards
the horizontal axis and the other awway from the
horizontal axis. The general shape and the two
turning points suggest that the algebraic curve
W = A+BX+CX 2 +DX 3 would be a good fit.
At start the curves are steep (i.e. make a big angle
with the horizontal axis) but later this angle de-
creases. This shows that the growth-rate is very
high in the beginning which falls off in later weeks.
Even at the end of one year the tendency of the
curves is that live-weight is on the increase. One
other feature of interest is that every curve showed
a downward curvature in summer months, suggest-
ing that winter is better than summer for the
growth of the kids. In order to test if the growth-
rate at any moment "was proportional to the live-
weight at that instant, the logarithms of weights
were plotted against time as before. The curves
were very irregular with only one concavity which
was turned towards the horizontal axis. If the
presumed law of growth were correct the curves
should have been straight lines.
The value of graphs is mostly of a suggestive
nature. We know much more about our data
when wo obtain the values of A, B, C, etc. in the
algebraic curve W = A+BX+CX 2 +DX 3 .
These
constants are so chosen that the departure of the
curve from the points to which the curve is fitted.
is least. It has been agreed to measure this de-
parture by the sum of the squares of the deviations
of individual points from the fitted curve. So to
choose the constants this sum of squares is made
least. This method of finding the constants of a
curve is called the method of least squares and is
due to Legendre. In the proposed curve the
highest power of × is three and so we call it a
parabola of third degree. Which degree parabola
would best fit our data cannot be decided merely
by looking at the graphs of growth-curves. There
-are better ways of deciding it. In this method the
degree of parabola is increased by stages and its
superiority over the lower degree is tested [Tippett
1931]. In this type of investigation, the curve is
put for convenience in a rather different form,
namely, W=a+bέ 1 +cέ 2 etc. where έ 1 =X—X
έ=έ1 2 —N 2 —1 /12 and X being the arithmetic mean
of X's and N being the number of observations
(in our case 24). These έ's are called the orthogonal
functions and are clue to Fisher [1936]. Proceed
ing in the above manner it was found that the
third degree parabola was significantly better
than the first, or fourth degree parabola. ' Signi
ficantly better ' denotes that the differences were
115