An Introduction to
Statistics with Klong
χ^{2} Tests and Contingency Tables
The nstat
module has builtin support for
χ^{2} tests.
Given a data set of
observations
(O) and a data set of corresponding
expectations
(E), the X2
function can be used to
compute the resulting
χ^{2} statistic
and, subsequently, the
improbability
of the statistic given the
null hypothesis
O=E.
E::[10 10 10 10 10 10]
O::[ 7 13 12 8 15 5]
X2(E;O)
7.6
x2.cdf(5;it)
0.820298060986649229

The expectation of a
contingency table
is computed by the
ct.exp
function (results in the output have been
rounded to one decimal place):
CT::[[47 23 51 27]
[52 28 45 25]
[20 37 21 23]]
ct.exp(CT)
[[44.1 32.6 43.4 27.8]
[44.7 33.1 44.0 28.2]
[30.1 22.3 29.6 19.0]]

The corresponding χ^{2} statistic is computed by
ct.X2
:
ct.X2(CT)
23.2250278064831061

For the curious:
x2.cdf(6;ct.X2(CT))
0.999275490338781315

So getting results (at least) as far removed from the expectation as
in above table is pretty unlikely.
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