Sheep - AgRIS

The Coefficient of Variation
The coefficient of variation is another method of expressing the amount of variation within
a particular population. When this coefficient is multiplied by 100, it is expressed as a
percentage. The coefficient of variation is the fraction or percentage tllat the standard deviation
is of the mean. One important use of this statistic is that it can be used to compare the variations
oftwo unrelated groups.
Standard Deviation of the Mean
In experimental work with livestock, we do not use an unlimited or indefinite number of
animals. Actually, we use a very small sample of the entire population. This is true even if the
sample includes the hundreds of animals for a given experiment. For ascertaining the closeness
of the mean of the sample with the true mean of the entire population.
We use a method of calculating approximately the true mean of the population, and this
statistic is called the Standard Deviation of the Mean (S.E.). The standard deviation of the mean
may be determined by dividing the standard deviation of the distribution (S.D.) by the square
root of the number of items in the population. The formula can thus be written:
S.E = S.D.
n
We can use the standard deviation of the mean together with the mean of the
distribution to describe the true mean of an infinite number of means drawn from a
population. The mean of the distribution plus or minus one S.E. should include about
68 per cent of the means. The mean of the distribution plus or minus two S.E. should
include approximately 95 per cent of the means. In other words, we can say that there
are only 5 chances out of 100 that the true mean of an infinite number of means drawn
from a population would fall outside the mean of a sample plus or minus two S.E.
Quite often in scientific reports.The mean of a sarnple is reported together with plus or
minus the S.E.
If the means of two large samples have been derived independently, the information can be
used to determine the Standard Deviation of a Difference of means.,l The formula for this is:
(S.E. 1 ) 2 + (S.E. 2 ) 2
If a difference between the means of two samples is at least twice as large as the Standard
Deviation of the Difference, we can acceptthis as atrue difference atthe five per cent level of
probability.
Coefficient of Correlation
This statistic and the expansion of the idea are often used in animal breeding and livestock
production research. The co-efficient of correlation is referred to as r and gives a measure of
how two variables tend to move together. They are said to be positively correlated if they tend
to move together in the same direction; i.e., when one increases the other increases, or when
one decreases the other decreases. They are said to be negatively correlated if they tend to
move together in the same direction, that is, when one increases the other increases, or when
one decreases the other decreases. They are said to be negatively correlated if they tend to
move in opposite directions i.e., when one increases the other decreases. Thus, the coefficient
of correlation for two variables lies somewhere between zero and ±1.
Although the coefficient of correlation tells us how two variables tend to move together in
like or in opposite directions, it does not necessarily mean that the movement of onc is the
cause or the effect of the movement of the other. The cause and effect relationship must be
determined, if possible, from other known facts concerning these two variables.
A particular coefficient of correlation is usually said to be significant, highly significant, or
nonsignificant, the degree of significance depending upon the size of the coefficient of
correlation and he number of individual items used to calculate it.
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