chiSquare(double[] expected, long[] observed) is returning incorrect test
statistic
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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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