[jira] Resolved: (MATH-175) chiSquare(double[] expected, long[] observed) is returning incorrect test statistic

["Phil Steitz (JIRA)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/MATH-175?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Phil Steitz resolved MATH-175.
------------------------------

    Resolution: Fixed

Automatic rescaling fix committed in r610274. 

> chiSquare(double[] expected, long[] observed) is returning incorrect test statistic
> -----------------------------------------------------------------------------------
>
>                 Key: MATH-175
>                 URL: https://issues.apache.org/jira/browse/MATH-175
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 1.1
>         Environment: windows xp
>            Reporter: carl anderson
>             Fix For: 1.2
>
>         Attachments: chi.xls
>
>
> ChiSquareTestImpl is returning incorrect chi-squared value. An implicit assumption of public double chiSquare(double[] expected, long[] observed) is that the sum of expected and observed are equal. That is, in the code:
> for (int i = 0; i < observed.length; i++) {
>             dev = ((double) observed[i] - expected[i]);
>             sumSq += dev * dev / expected[i];
>         }
> this calculation is only correct if sum(observed)==sum(expected). When they are not equal then one must rescale the expected value by sum(observed) / sum(expected) so that they are.
> Ironically, it is an example in the unit test ChiSquareTestTest that highlights the error:
> long[] observed1 = { 500, 623, 72, 70, 31 };
>         double[] expected1 = { 485, 541, 82, 61, 37 };
>         assertEquals( "chi-square test statistic", 16.4131070362, testStatistic.chiSquare(expected1, observed1), 1E-10);
>         assertEquals("chi-square p-value", 0.002512096, testStatistic.chiSquareTest(expected1, observed1), 1E-9);
> 16.413 is not correct because the expected values do not make sense, they should be: 521.19403 581.37313  88.11940  65.55224  39.76119 so that the sum of expected equals 1296 which is the sum of observed.
> Here is some R code (r-project.org) which proves it:
> > o1
> [1] 500 623  72  70  31
> > e1
> [1] 485 541  82  61  37
> > chisq.test(o1,p=e1,rescale.p=TRUE)
>         Chi-squared test for given probabilities
> data:  o1 
> X-squared = 9.0233, df = 4, p-value = 0.06052
> > chisq.test(o1,p=e1,rescale.p=TRUE)$observed
> [1] 500 623  72  70  31
> > chisq.test(o1,p=e1,rescale.p=TRUE)$expected
> [1] 521.19403 581.37313  88.11940  65.55224  39.76119
>  

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