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From "carl anderson (JIRA)" <j...@apache.org>
Subject [jira] Created: (MATH-175) chiSquare(double[] expected, long[] observed) is returning incorrect test statistic
Date Tue, 04 Dec 2007 02:32:43 GMT
```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

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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