public class ChiSquareTest extends Object
This implementation handles both, known and unknown distributions.
Two samples tests are used when the distribution is unknown a priori but provided by one sample. We compare the second sample against the first.
Constructor and Description 

ChiSquareTest()
Construct a ChiSquareTest

Modifier and Type  Method and Description 

double 
chiSquare(double[] expected,
long[] observed)

double 
chiSquare(long[][] counts)
Computes the ChiSquare statistic associated with a
chisquare test of independence based on the input
counts
array, viewed as a twoway table. 
double 
chiSquareDataSetsComparison(long[] observed1,
long[] observed2)
Computes a
ChiSquare two sample test statistic comparing bin frequency counts
in
observed1 and observed2 . 
double 
chiSquareTest(double[] expected,
long[] observed)
Returns the observed significance level, or
pvalue, associated with a
Chisquare goodness of fit test comparing the
observed
frequency counts to those in the expected array. 
boolean 
chiSquareTest(double[] expected,
long[] observed,
double alpha)
Performs a
Chisquare goodness of fit test evaluating the null hypothesis that the
observed counts conform to the frequency distribution described by the expected
counts, with significance level
alpha . 
double 
chiSquareTest(long[][] counts)
Returns the observed significance level, or
pvalue, associated with a
chisquare test of independence based on the input
counts
array, viewed as a twoway table. 
boolean 
chiSquareTest(long[][] counts,
double alpha)
Performs a
chisquare test of independence evaluating the null hypothesis that the
classifications represented by the counts in the columns of the input 2way table
are independent of the rows, with significance level
alpha . 
double 
chiSquareTestDataSetsComparison(long[] observed1,
long[] observed2)
Returns the observed significance level, or
pvalue, associated with a ChiSquare two sample test comparing
bin frequency counts in
observed1 and
observed2 . 
boolean 
chiSquareTestDataSetsComparison(long[] observed1,
long[] observed2,
double alpha)
Performs a ChiSquare two sample test comparing two binned data
sets.

public double chiSquare(double[] expected, long[] observed) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException
observed
and expected
frequency counts.
This statistic can be used to perform a ChiSquare test evaluating the null hypothesis that the observed counts follow the expected distribution.
Preconditions:
If any of the preconditions are not met, an
IllegalArgumentException
is thrown.
Note: This implementation rescales the
expected
array if necessary to ensure that the sum of the
expected and observed counts are equal.
observed
 array of observed frequency countsexpected
 array of expected frequency countsNotPositiveException
 if one element of expected
is not
positiveNotStrictlyPositiveException
 if one element of observed
is
not strictly positiveDimensionMismatchException
 if the arrays length is less than 2public double chiSquareTest(double[] expected, long[] observed) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException, MaxCountExceededException
observed
frequency counts to those in the expected
array.
The number returned is the smallest significance level at which one can reject the null hypothesis that the observed counts conform to the frequency distribution described by the expected counts.
Preconditions:
If any of the preconditions are not met, an
IllegalArgumentException
is thrown.
Note: This implementation rescales the
expected
array if necessary to ensure that the sum of the
expected and observed counts are equal.
observed
 array of observed frequency countsexpected
 array of expected frequency countsNotPositiveException
 if one element of expected
is not
positiveNotStrictlyPositiveException
 if one element of observed
is
not strictly positiveDimensionMismatchException
 if the arrays length is less than 2MaxCountExceededException
 if an error occurs computing the pvaluepublic boolean chiSquareTest(double[] expected, long[] observed, double alpha) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException, OutOfRangeException, MaxCountExceededException
alpha
. Returns true iff the null
hypothesis can be rejected with 100 * (1  alpha) percent confidence.
Example:
To test the hypothesis that observed
follows
expected
at the 99% level, use
chiSquareTest(expected, observed, 0.01)
Preconditions:
0 < alpha < 0.5
If any of the preconditions are not met, an
IllegalArgumentException
is thrown.
Note: This implementation rescales the
expected
array if necessary to ensure that the sum of the
expected and observed counts are equal.
observed
 array of observed frequency countsexpected
 array of expected frequency countsalpha
 significance level of the testNotPositiveException
 if one element of expected
is not
positiveNotStrictlyPositiveException
 if one element of observed
is
not strictly positiveDimensionMismatchException
 if the arrays length is less than 2OutOfRangeException
 if alpha
is not in the range (0, 0.5]MaxCountExceededException
 if an error occurs computing the pvaluepublic double chiSquare(long[][] counts) throws NullArgumentException, NotPositiveException, DimensionMismatchException
counts
array, viewed as a twoway table.
The rows of the 2way table are
count[0], ... , count[count.length  1]
Preconditions:
counts
must have at
least 2 columns and at least 2 rows.
If any of the preconditions are not met, an
IllegalArgumentException
is thrown.
counts
 array representation of 2way tableNullArgumentException
 if the array is nullDimensionMismatchException
 if the array is not rectangularNotPositiveException
 if one entry is not positivepublic double chiSquareTest(long[][] counts) throws NullArgumentException, DimensionMismatchException, NotPositiveException, MaxCountExceededException
counts
array, viewed as a twoway table.
The rows of the 2way table are
count[0], ... , count[count.length  1]
Preconditions:
counts
must have at least 2
columns and at least 2 rows.
If any of the preconditions are not met, an
IllegalArgumentException
is thrown.
counts
 array representation of 2way tableNullArgumentException
 if the array is nullDimensionMismatchException
 if the array is not rectangularNotPositiveException
 if one entry is not positiveMaxCountExceededException
 if an error occurs computing the pvaluepublic boolean chiSquareTest(long[][] counts, double alpha) throws NullArgumentException, DimensionMismatchException, NotPositiveException, OutOfRangeException, MaxCountExceededException
alpha
.
Returns true iff the null hypothesis can be rejected with 100 * (1  alpha) percent
confidence.
The rows of the 2way table are
count[0], ... , count[count.length  1]
Example:
To test the null hypothesis that the counts in
count[0], ... , count[count.length  1]
all correspond to the same underlying probability distribution at the 99% level, use
chiSquareTest(counts, 0.01)
Preconditions:
counts
must have at least 2 columns and
at least 2 rows.
If any of the preconditions are not met, an
IllegalArgumentException
is thrown.
counts
 array representation of 2way tablealpha
 significance level of the testNullArgumentException
 if the array is nullDimensionMismatchException
 if the array is not rectangularNotPositiveException
 if one entry is not positiveOutOfRangeException
 if alpha
is not in the range (0, 0.5]MaxCountExceededException
 if an error occurs computing the pvaluepublic double chiSquareDataSetsComparison(long[] observed1, long[] observed2) throws DimensionMismatchException, NotPositiveException, ZeroException
Computes a
ChiSquare two sample test statistic comparing bin frequency counts
in observed1
and observed2
. The
sums of frequency counts in the two samples are not required to be the
same. The formula used to compute the test statistic is
∑[(K * observed1[i]  observed2[i]/K)^{2} / (observed1[i] + observed2[i])]
where
K = &sqrt;[&sum(observed2 / ∑(observed1)]
This statistic can be used to perform a ChiSquare test evaluating the null hypothesis that both observed counts follow the same distribution.
Preconditions:
observed1
and observed2
must have
the same length and their common length must be at least 2.
If any of the preconditions are not met, an
IllegalArgumentException
is thrown.
observed1
 array of observed frequency counts of the first data setobserved2
 array of observed frequency counts of the second data setDimensionMismatchException
 the the length of the arrays does not matchNotPositiveException
 if one entry in observed1
or
observed2
is not positiveZeroException
 if either all counts of observed1
or
observed2
are zero, or if the count at the same index is zero
for both arrayspublic double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2) throws DimensionMismatchException, NotPositiveException, ZeroException, MaxCountExceededException
Returns the observed significance level, or
pvalue, associated with a ChiSquare two sample test comparing
bin frequency counts in observed1
and
observed2
.
The number returned is the smallest significance level at which one can reject the null hypothesis that the observed counts conform to the same distribution.
See chiSquareDataSetsComparison(long[], long[])
for details
on the formula used to compute the test statistic. The degrees of
of freedom used to perform the test is one less than the common length
of the input observed count arrays.
observed1
and observed2
must
have the same length and
their common length must be at least 2.
If any of the preconditions are not met, an
IllegalArgumentException
is thrown.
observed1
 array of observed frequency counts of the first data setobserved2
 array of observed frequency counts of the second data setDimensionMismatchException
 the the length of the arrays does not matchNotPositiveException
 if one entry in observed1
or
observed2
is not positiveZeroException
 if either all counts of observed1
or
observed2
are zero, or if the count at the same index is zero
for both arraysMaxCountExceededException
 if an error occurs computing the pvaluepublic boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha) throws DimensionMismatchException, NotPositiveException, ZeroException, OutOfRangeException, MaxCountExceededException
Performs a ChiSquare two sample test comparing two binned data
sets. The test evaluates the null hypothesis that the two lists of
observed counts conform to the same frequency distribution, with
significance level alpha
. Returns true iff the null
hypothesis can be rejected with 100 * (1  alpha) percent confidence.
See chiSquareDataSetsComparison(long[], long[])
for
details on the formula used to compute the Chisquare statistic used
in the test. The degrees of of freedom used to perform the test is
one less than the common length of the input observed count arrays.
observed1
and observed2
must
have the same length and their common length must be at least 2.
0 < alpha < 0.5
If any of the preconditions are not met, an
IllegalArgumentException
is thrown.
observed1
 array of observed frequency counts of the first data setobserved2
 array of observed frequency counts of the second data setalpha
 significance level of the testDimensionMismatchException
 the the length of the arrays does not matchNotPositiveException
 if one entry in observed1
or
observed2
is not positiveZeroException
 if either all counts of observed1
or
observed2
are zero, or if the count at the same index is zero
for both arraysOutOfRangeException
 if alpha
is not in the range (0, 0.5]MaxCountExceededException
 if an error occurs performing the testCopyright © 20032012 The Apache Software Foundation. All Rights Reserved.