Abstract
If
x
1
...
x
n
are the values of a variate observed in a sample of
n
, from any population, we may evaluate a series of statistics (
K
) such that the mean value of
k
p
will be the
p
th cumulative moment function of the sampled population; the first three of these are defined by the equations;
k
1
= 1/
n
S (
x
),
k
2
= 1/
n
-1 S (
x
-
k
1
)
2
,
k
3
=
n
/(
n
-1) (
n
-2) S (
x
-
k
1
)
3
; then it has been shown (fisher, 1929) that the cumulative moment functions of the simultaneous distribution, in samples, of
k
1
,
k
2
,
k
3
,..., may be obtained by the direct application of a very simple combination procedure. The simplest measure of departure from normality will the be γ =
k
3
k
2
-3/2
, a quantity which is evidently independent of the units of measurements, and in samples from a symmetrical distribution will have a distribution symmetrical about the value zero. In testing the evidence provided by a sample, of departure from normality, the distribution of this quantity in normal samples is required.
Cited by
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