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https://issues.apache.org/jira/browse/MATH-175?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel#action_12548526
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Phil Steitz commented on MATH-175:
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Thank you for reporting this. I agree that if the count sums are unequal, the
test is not meaningful (at least I can't see a meaningful interpretation). So
the question is, do we throw IllegalArgumentException in this case or assume
expected should be rescaled?
> 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
> [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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