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CHI2TEST2

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Two-sample chi-squared test for discrete data.

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  H = CHI2TEST2(X) performs a chi-squared two-sample test of the
  similarity of two samples, under the null hypothesis that two samples
  come from the same (non-specified) distribution.

  X1 and X2 are two vectors containing discrete (categorical) data.
  CHI2TEST2 treats all unique values as separate 'bins' for testing
  purposes. X1 and X2 can be different lengths. CHI2TEST2 treats NaNs as
  missing values, and ignores them.

  H = TTEST(...,ALPHA) performs the test at the significance level
  (100*ALPHA)%. ALPHA must be a scalar. Default value of ALPHA is 0.05.
  i.e., H = 1 suggests different distributions.

  [H,P] = TTEST(...) returns the p-value, i.e., the probability of
  observing the given result, or one more extreme, by chance if the null
  hypothesis is true. Small values of P cast doubt on the validity of
  the null hypothesis (i.e. suggests different distributions).

  [H,P,TEST] = TTEST(...) returns TEST, the value of the test statistic.

  [H,P,TEST,DF] = TTEST(...) returns DF, the degrees of freedom of the test.

  EXAMPLE 1: Generate two uniform random vectors, should be H = 0
      rng('default')
      x1 = round(rand(1000,1)*10);
      x2 = round(rand(1000,1)*10);
      [h,p,test,df] = chi2test2(x1,x2)
            h =
                 0
            p =
                0.4505
            test =
                9.8868
            df =
                10

  EXAMPLE 2: Generate two random vectors, one uniform and one normal,
  should be H = 1
      rng('default')
      x1 = round(rand(1000,1)*10);
      x2 = 5 + round(randn(1000,1));
      [h,p,test,df] = chi2test2(x1,x2)
            h =
                1
            p =
                0
            test =
                758.0990
            df =
                10
                

  Reference:
  http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/chi2samp.htm
          Accessed March 29, 2013, and cites: "Numerical Recipes in
          Fortan: The Art of Scientific Computing", Second Edition,
          Press, Teukolsky, Vetterlling, and Flannery, Cambridge
          University Press, 1992, pp. 614-622.

  Copyright 2013 James Meldrum. Provided for entertainment only; author
  is not responsible for any use or misuse of code. Verify before use!
  Revision: 1, 2013/03/29 $

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