org.apache.commons.math3.stat.inference.ChiSquareTest
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java.lang.Object
public class ChiSquareTest
Implements Chi-Square test statistics.
This implementation handles both known and unknown distributions.
Two samples tests can be used when the distribution is unknown a priori but provided by one sample, or when the hypothesis under test is that the two samples come from the same underlying distribution.
| Constructor Summary | |
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ChiSquareTest()
Construct a ChiSquareTest |
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| Method Summary | |
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double |
chiSquare(double[] expected,
long[] observed)
Computes the Chi-Square statistic comparing observed and expected
frequency counts. |
double |
chiSquare(long[][] counts)
Computes the Chi-Square statistic associated with a chi-square test of independence based on the input counts
array, viewed as a two-way table. |
double |
chiSquareDataSetsComparison(long[] observed1,
long[] observed2)
Computes a Chi-Square two sample test statistic comparing bin frequency counts in observed1 and observed2. |
double |
chiSquareTest(double[] expected,
long[] observed)
Returns the observed significance level, or p-value, associated with a Chi-square 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 Chi-square 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 p-value, associated with a chi-square test of independence based on the input counts
array, viewed as a two-way table. |
boolean |
chiSquareTest(long[][] counts,
double alpha)
Performs a chi-square test of independence evaluating the null hypothesis that the classifications represented by the counts in the columns of the input 2-way table are independent of the rows, with significance level alpha. |
double |
chiSquareTestDataSetsComparison(long[] observed1,
long[] observed2)
Returns the observed significance level, or p-value, associated with a Chi-Square two sample test comparing bin frequency counts in observed1 and
observed2. |
boolean |
chiSquareTestDataSetsComparison(long[] observed1,
long[] observed2,
double alpha)
Performs a Chi-Square two sample test comparing two binned data sets. |
| Methods inherited from class java.lang.Object |
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clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Constructor Detail |
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public ChiSquareTest()
| Method Detail |
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public double chiSquare(double[] expected,
long[] observed)
throws NotPositiveException,
NotStrictlyPositiveException,
DimensionMismatchException
observed and expected
frequency counts.
This statistic can be used to perform a Chi-Square 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 counts
NotPositiveException - if observed has negative entries
NotStrictlyPositiveException - if expected has entries that are
not strictly positive
DimensionMismatchException - if the arrays length is less than 2
public 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 counts
NotPositiveException - if observed has negative entries
NotStrictlyPositiveException - if expected has entries that are
not strictly positive
DimensionMismatchException - if the arrays length is less than 2
MaxCountExceededException - if an error occurs computing the p-value
public 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 test
NotPositiveException - if observed has negative entries
NotStrictlyPositiveException - if expected has entries that are
not strictly positive
DimensionMismatchException - if the arrays length is less than 2
OutOfRangeException - if alpha is not in the range (0, 0.5]
MaxCountExceededException - if an error occurs computing the p-value
public double chiSquare(long[][] counts)
throws NullArgumentException,
NotPositiveException,
DimensionMismatchException
counts
array, viewed as a two-way table.
The rows of the 2-way 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 2-way table
NullArgumentException - if the array is null
DimensionMismatchException - if the array is not rectangular
NotPositiveException - if counts has negative entries
public double chiSquareTest(long[][] counts)
throws NullArgumentException,
DimensionMismatchException,
NotPositiveException,
MaxCountExceededException
counts
array, viewed as a two-way table.
The rows of the 2-way 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 2-way table
NullArgumentException - if the array is null
DimensionMismatchException - if the array is not rectangular
NotPositiveException - if counts has negative entries
MaxCountExceededException - if an error occurs computing the p-value
public 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 2-way 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 2-way tablealpha - significance level of the test
NullArgumentException - if the array is null
DimensionMismatchException - if the array is not rectangular
NotPositiveException - if counts has any negative entries
OutOfRangeException - if alpha is not in the range (0, 0.5]
MaxCountExceededException - if an error occurs computing the p-value
public double chiSquareDataSetsComparison(long[] observed1,
long[] observed2)
throws DimensionMismatchException,
NotPositiveException,
ZeroException
Computes a
Chi-Square 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 Chi-Square 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 set
DimensionMismatchException - the the length of the arrays does not match
NotPositiveException - if any entries in observed1 or
observed2 are negative
ZeroException - if either all counts of observed1 or
observed2 are zero, or if the count at some index is zero
for both arrays
public double chiSquareTestDataSetsComparison(long[] observed1,
long[] observed2)
throws DimensionMismatchException,
NotPositiveException,
ZeroException,
MaxCountExceededException
Returns the observed significance level, or
p-value, associated with a Chi-Square 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 set
DimensionMismatchException - the the length of the arrays does not match
NotPositiveException - if any entries in observed1 or
observed2 are negative
ZeroException - if either all counts of observed1 or
observed2 are zero, or if the count at the same index is zero
for both arrays
MaxCountExceededException - if an error occurs computing the p-value
public boolean chiSquareTestDataSetsComparison(long[] observed1,
long[] observed2,
double alpha)
throws DimensionMismatchException,
NotPositiveException,
ZeroException,
OutOfRangeException,
MaxCountExceededException
Performs a Chi-Square 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 test
DimensionMismatchException - the the length of the arrays does not match
NotPositiveException - if any entries in observed1 or
observed2 are negative
ZeroException - if either all counts of observed1 or
observed2 are zero, or if the count at the same index is zero
for both arrays
OutOfRangeException - if alpha is not in the range (0, 0.5]
MaxCountExceededException - if an error occurs performing the test
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