=begin

From http://en.wikipedia.org/wiki/Pearson's_chi-squared_test

Pearson's chi-squared test is used to assess whether paired observations on two
variables, expressed in a contingency table, are independent of each other.

An "observation" consists of the values of two outcomes and the null hypothesis
is that the occurrence of these outcomes is statistically independent. Each
observation is allocated to one cell of a two-dimensional array of cells (called
a contingency table) according to the values of the two outcomes.

Assumptions
-----------

The chi-squared test, when used with the standard approximation that a chi-
squared distribution is applicable, has the following assumptions:

* Simple random sample – The sample data is a random sampling from a fixed
  distribution or population where every collection of members of the population
  of the given sample size has an equal probability of selection. Variants of
  the test have been developed for complex samples, such as where the data is
  weighted. Other forms can be used such as purposive sampling.
* Sample size (whole table) – A sample with a sufficiently large size is assumed.
  If a chi squared test is conducted on a sample with a smaller size, then the
  chi squared test will yield an inaccurate inference. The researcher, by using
  chi squared test on small samples, might end up committing a Type II error.
* Expected cell count – Adequate expected cell counts. Some require 5 or more,
  and others require 10 or more. A common rule is 5 or more in all cells of a
  2-by-2 table, and 5 or more in 80% of cells in larger tables, but no cells
  with zero expected count. When this assumption is not met, Yates's Correction
  is applied.
* Independence – The observations are always assumed to be independent of each
  other. This means chi-squared cannot be used to test correlated data
  (like matched pairs or panel data). In those cases you might want to turn to
  McNemar's test.

Problems
--------

The approximation to the chi-squared distribution breaks down if expected
frequencies are too low. It will normally be acceptable so long as no more than
20% of the events have expected frequencies below 5. Where there is only 1
degree of freedom, the approximation is not reliable if expected frequencies are
below 10. In this case, a better approximation can be obtained by reducing the
absolute value of each difference between observed and expected frequencies by
0.5 before squaring; this is called Yates's correction for continuity.

In cases where the expected value, E, is found to be small (indicating a small
underlying population probability, and/or a small number of observations), the
normal approximation of the multinomial distribution can fail, and in such cases
it is found to be more appropriate to use the G-test, a likelihood ratio-based
test statistic. Where the total sample size is small, it is necessary to use an
appropriate exact test, typically either the binomial test or (for contingency
tables) Fisher's exact test. This test uses the conditional distribution of the
test statistic given the marginal totals; however, it does not assume that the
data were generated from an experiment in which the marginal totals are fixed
and is valid whether or not that is the case.

=end

class RailsDataExplorer
  module Statistics
    class PearsonsChiSquaredIndependenceTest

      #
      def initialize(data_matrix, min_probability = 0.05)
      end

      def compute
      end

    end
  end
end