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From "carl anderson (JIRA)" <j...@apache.org>
Subject [jira] Updated: (MATH-175) chiSquare(double[] expected, long[] observed) is returning incorrect test statistic
Date Tue, 04 Dec 2007 02:34:42 GMT
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[ https://issues.apache.org/jira/browse/MATH-175?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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carl anderson updated MATH-175:
-------------------------------

Attachment: chi.xls

here is the calculations currently in the code, and below the correct calculations

> 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
>         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
>  500 623  72  70  31
> > e1
>  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
>  500 623  72  70  31
> > chisq.test(o1,p=e1,rescale.p=TRUE)\$expected
>  521.19403 581.37313  88.11940  65.55224  39.76119
>

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