Apache Commons Math 3.6.1 · org.apache.commons.math3.stat.inference.ChiSquareTest

Access	Constructor and Description
public	ChiSquareTest() Construct a ChiSquareTest

Method Summary

Modifier and Type	Method and Description
private void	checkArray(final long[][] input 2-way table to check in) Checks to make sure that the input long[][] array is rectangular, has at least 2 rows and 2 columns, and has all non-negative entries.
public double	Returns: chiSquare test statistic chiSquare(final double[] array of expected frequency counts expected, final long[] array of observed frequency counts observed) Computes the Chi-Square statistic comparing `observed` and `expected` frequency counts.
public double	Returns: chiSquare test statistic chiSquare(final long[][] array representation of 2-way table 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.
public double	Returns: chiSquare test statistic chiSquareDataSetsComparison(long[] array of observed frequency counts of the first data set observed1, long[] array of observed frequency counts of the second data set observed2) Computes a Chi-Square two sample test statistic comparing bin frequency counts in `observed1` and `observed2`.
public double	Returns: p-value chiSquareTest(final double[] array of expected frequency counts expected, final long[] array of observed frequency counts 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.
public boolean	Returns: true iff null hypothesis can be rejected with confidence 1 - alpha chiSquareTest(final double[] array of expected frequency counts expected, final long[] array of observed frequency counts observed, final double significance level of the test 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`.
public double	Returns: p-value chiSquareTest(final long[][] array representation of 2-way table 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.
public boolean	Returns: true iff null hypothesis can be rejected with confidence 1 - alpha chiSquareTest(final long[][] array representation of 2-way table counts, final double significance level of the test 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`.
public double	Returns: p-value chiSquareTestDataSetsComparison(long[] array of observed frequency counts of the first data set observed1, long[] array of observed frequency counts of the second data set 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`.
public boolean	Returns: true iff null hypothesis can be rejected with confidence 1 - alpha chiSquareTestDataSetsComparison(final long[] array of observed frequency counts of the first data set observed1, final long[] array of observed frequency counts of the second data set observed2, final double significance level of the test alpha) Performs a Chi-Square two sample test comparing two binned data sets.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

ChiSquareTest	back to summary
public ChiSquareTest() Construct a ChiSquareTest

Method Detail

checkArray	back to summary
private void checkArray(final long[][] in) throws NullArgumentException, DimensionMismatchException, NotPositiveException Checks to make sure that the input long[][] array is rectangular, has at least 2 rows and 2 columns, and has all non-negative entries. Parameters in:long[][] input 2-way table to check Exceptions NullArgumentException: if the array is null DimensionMismatchException: if the array is not valid NotPositiveException: if the array contains any negative entries

checkArray

back to summary

private void checkArray(final long[][] in) throws NullArgumentException, DimensionMismatchException, NotPositiveException

Checks to make sure that the input long[][] array is rectangular, has at least 2 rows and 2 columns, and has all non-negative entries.

Parameters

in:long[][]: input 2-way table to check

Exceptions

NullArgumentException:: if the array is null
DimensionMismatchException:: if the array is not valid
NotPositiveException:: if the array contains any negative entries

chiSquare back to summary

chiSquare	back to summary
public double chiSquare(final double[] expected, final long[] observed) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException Computes the Chi-Square statistic comparing `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: Expected counts must all be positive. Observed counts must all be ≥ 0. The observed and expected arrays 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. Note This implementation rescales the `expected` array if necessary to ensure that the sum of the expected and observed counts are equal. Parameters expected:double[] array of expected frequency counts observed:long[] array of observed frequency counts Returns:double chiSquare test statistic Exceptions 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 chiSquare(final double[] expected, final long[] observed) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException

Computes the Chi-Square statistic comparing 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:

Expected counts must all be positive.
Observed counts must all be ≥ 0.
The observed and expected arrays 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.

Note

This implementation rescales the expected array if necessary to ensure that the sum of the expected and observed counts are equal.

Parameters

expected:double[]: array of expected frequency counts
observed:long[]: array of observed frequency counts

Returns:double

chiSquare test statistic

Exceptions

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

chiSquare back to summary

chiSquare	back to summary
public double chiSquare(final long[][] counts) throws NullArgumentException, NotPositiveException, DimensionMismatchException 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. The rows of the 2-way table are `count[0], ... , count[count.length - 1]` Preconditions: All counts must be ≥ 0. The count array must be rectangular (i.e. all count[i] subarrays must have the same length). The 2-way table represented by `counts` must have at least 2 columns and at least 2 rows. If any of the preconditions are not met, an `IllegalArgumentException` is thrown. Parameters counts:long[][] array representation of 2-way table Returns:double chiSquare test statistic Exceptions NullArgumentException: if the array is null NotPositiveException: if `counts` has negative entries DimensionMismatchException: if the array is not rectangular

public double chiSquare(final long[][] counts) throws NullArgumentException, NotPositiveException, DimensionMismatchException

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.

The rows of the 2-way table are count[0], ... , count[count.length - 1]

Preconditions:

All counts must be ≥ 0.
The count array must be rectangular (i.e. all count[i] subarrays must have the same length).
The 2-way table represented by counts must have at least 2 columns and at least 2 rows.

If any of the preconditions are not met, an IllegalArgumentException is thrown.

Parameters

counts:long[][]: array representation of 2-way table

Returns:double

chiSquare test statistic

Exceptions

NullArgumentException:: if the array is null
NotPositiveException:: if counts has negative entries
DimensionMismatchException:: if the array is not rectangular

chiSquareDataSetsComparison back to summary

chiSquareDataSetsComparison	back to summary
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: Observed counts must be non-negative. Observed counts for a specific bin must not both be zero. Observed counts for a specific sample must not all be 0. The 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. Parameters observed1:long[] array of observed frequency counts of the first data set observed2:long[] array of observed frequency counts of the second data set Returns:double chiSquare test statistic Exceptions 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 Since 1.2

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:

Observed counts must be non-negative.
Observed counts for a specific bin must not both be zero.
Observed counts for a specific sample must not all be 0.
The 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.

Parameters

observed1:long[]: array of observed frequency counts of the first data set
observed2:long[]: array of observed frequency counts of the second data set

Returns:double

chiSquare test statistic

Exceptions

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

Since

1.2

chiSquareTest back to summary

chiSquareTest	back to summary
public double chiSquareTest(final double[] expected, final long[] observed) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException, MaxCountExceededException 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. 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: Expected counts must all be positive. Observed counts must all be ≥ 0. The observed and expected arrays 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. Note This implementation rescales the `expected` array if necessary to ensure that the sum of the expected and observed counts are equal. Parameters expected:double[] array of expected frequency counts observed:long[] array of observed frequency counts Returns:double p-value Exceptions 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 double chiSquareTest(final double[] expected, final long[] observed) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException, MaxCountExceededException

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.

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:

Expected counts must all be positive.
Observed counts must all be ≥ 0.
The observed and expected arrays 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.

Note

This implementation rescales the expected array if necessary to ensure that the sum of the expected and observed counts are equal.

Parameters

expected:double[]: array of expected frequency counts
observed:long[]: array of observed frequency counts

Returns:double

p-value

Exceptions

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

chiSquareTest back to summary

chiSquareTest	back to summary
public boolean chiSquareTest(final double[] expected, final long[] observed, final double alpha) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException, OutOfRangeException, MaxCountExceededException 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`. 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: Expected counts must all be positive. Observed counts must all be ≥ 0. The observed and expected arrays 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. Note This implementation rescales the `expected` array if necessary to ensure that the sum of the expected and observed counts are equal. Parameters expected:double[] array of expected frequency counts observed:long[] array of observed frequency counts alpha:double significance level of the test Returns:boolean true iff null hypothesis can be rejected with confidence 1 - alpha Exceptions 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 boolean chiSquareTest(final double[] expected, final long[] observed, final double alpha) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException, OutOfRangeException, MaxCountExceededException

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. 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:

Expected counts must all be positive.
Observed counts must all be ≥ 0.
The observed and expected arrays 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.

Note

This implementation rescales the expected array if necessary to ensure that the sum of the expected and observed counts are equal.

Parameters

expected:double[]: array of expected frequency counts
observed:long[]: array of observed frequency counts
alpha:double: significance level of the test

Returns:boolean

true iff null hypothesis can be rejected with confidence 1 - alpha

Exceptions

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

chiSquareTest back to summary

chiSquareTest	back to summary
public double chiSquareTest(final long[][] counts) throws NullArgumentException, DimensionMismatchException, NotPositiveException, MaxCountExceededException 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. The rows of the 2-way table are `count[0], ... , count[count.length - 1]` Preconditions: All counts must be ≥ 0. The count array must be rectangular (i.e. all count[i] subarrays must have the same length). The 2-way table represented by `counts` must have at least 2 columns and at least 2 rows. If any of the preconditions are not met, an `IllegalArgumentException` is thrown. Parameters counts:long[][] array representation of 2-way table Returns:double p-value Exceptions 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 double chiSquareTest(final long[][] counts) throws NullArgumentException, DimensionMismatchException, NotPositiveException, MaxCountExceededException

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.

The rows of the 2-way table are count[0], ... , count[count.length - 1]

Preconditions:

All counts must be ≥ 0.
The count array must be rectangular (i.e. all count[i] subarrays must have the same length).
The 2-way table represented by counts must have at least 2 columns and at least 2 rows.

If any of the preconditions are not met, an IllegalArgumentException is thrown.

Parameters

counts:long[][]: array representation of 2-way table

Returns:double

p-value

Exceptions

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

chiSquareTest back to summary

chiSquareTest	back to summary
public boolean chiSquareTest(final long[][] counts, final double alpha) throws NullArgumentException, DimensionMismatchException, NotPositiveException, OutOfRangeException, MaxCountExceededException 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`. 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: All counts must be ≥ 0. The count array must be rectangular (i.e. all count[i] subarrays must have the same length). The 2-way table represented by `counts` must have at least 2 columns and at least 2 rows. If any of the preconditions are not met, an `IllegalArgumentException` is thrown. Parameters counts:long[][] array representation of 2-way table alpha:double significance level of the test Returns:boolean true iff null hypothesis can be rejected with confidence 1 - alpha Exceptions 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 boolean chiSquareTest(final long[][] counts, final double alpha) throws NullArgumentException, DimensionMismatchException, NotPositiveException, OutOfRangeException, MaxCountExceededException

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. 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:

All counts must be ≥ 0.
The count array must be rectangular (i.e. all count[i] subarrays must have the same length).
The 2-way table represented by counts must have at least 2 columns and at least 2 rows.

If any of the preconditions are not met, an IllegalArgumentException is thrown.

Parameters

counts:long[][]: array representation of 2-way table
alpha:double: significance level of the test

Returns:boolean

true iff null hypothesis can be rejected with confidence 1 - alpha

Exceptions

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

chiSquareTestDataSetsComparison back to summary

chiSquareTestDataSetsComparison	back to summary
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. Preconditions: Observed counts must be non-negative. Observed counts for a specific bin must not both be zero. Observed counts for a specific sample must not all be 0. The 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. Parameters observed1:long[] array of observed frequency counts of the first data set observed2:long[] array of observed frequency counts of the second data set Returns:double p-value Exceptions 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 Since 1.2

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.

Preconditions:

Observed counts must be non-negative.
Observed counts for a specific bin must not both be zero.
Observed counts for a specific sample must not all be 0.
The 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.

Parameters

observed1:long[]: array of observed frequency counts of the first data set
observed2:long[]: array of observed frequency counts of the second data set

Returns:double

p-value

Exceptions

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

Since

1.2

chiSquareTestDataSetsComparison back to summary

chiSquareTestDataSetsComparison	back to summary
public boolean chiSquareTestDataSetsComparison(final long[] observed1, final long[] observed2, final 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. Preconditions: Observed counts must be non-negative. Observed counts for a specific bin must not both be zero. Observed counts for a specific sample must not all be 0. The 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. Parameters observed1:long[] array of observed frequency counts of the first data set observed2:long[] array of observed frequency counts of the second data set alpha:double significance level of the test Returns:boolean true iff null hypothesis can be rejected with confidence 1 - alpha Exceptions 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 Since 1.2

public boolean chiSquareTestDataSetsComparison(final long[] observed1, final long[] observed2, final 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.

Preconditions:

Observed counts must be non-negative.
Observed counts for a specific bin must not both be zero.
Observed counts for a specific sample must not all be 0.
The 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.

Parameters

observed1:long[]: array of observed frequency counts of the first data set
observed2:long[]: array of observed frequency counts of the second data set
alpha:double: significance level of the test

Returns:boolean

true iff null hypothesis can be rejected with confidence 1 - alpha

Exceptions

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

Since

1.2

public Class ChiSquareTest

Constructor Summary

Method Summary

Constructor Detail

Method Detail