An Introduction to
Statistics with Klong

χ² Tests and Contingency Tables

The nstat module has built-in support for χ² 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 χ² 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 χ² 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.