Package org.apache.commons.math4.legacy.stat.inference

Class BinomialTest

java.lang.Object

org.apache.commons.math4.legacy.stat.inference.BinomialTest

public class BinomialTest
extends Object

Implements binomial test statistics.

Exact test for the statistical significance of deviations from a theoretically expected distribution of observations into two categories.

Since:

3.3

See Also:

Binomial test (Wikipedia)

Constructor Summary

Constructors

Constructor	Description
BinomialTest()

Method Summary

Modifier and Type	Method	Description
double	binomialTest(int numberOfTrials, int numberOfSuccesses, double probability, AlternativeHypothesis alternativeHypothesis)	Returns the observed significance level, or p-value, associated with a Binomial test.
boolean	binomialTest(int numberOfTrials, int numberOfSuccesses, double probability, AlternativeHypothesis alternativeHypothesis, double alpha)	Returns whether the null hypothesis can be rejected with the given confidence level.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

BinomialTest

public BinomialTest()

Method Detail

binomialTest

public boolean binomialTest(int numberOfTrials,
                            int numberOfSuccesses,
                            double probability,
                            AlternativeHypothesis alternativeHypothesis,
                            double alpha)

Returns whether the null hypothesis can be rejected with the given confidence level.

Preconditions:

• Number of trials must be ≥ 0.
• Number of successes must be ≥ 0.
• Number of successes must be ≤ number of trials.
• Probability must be ≥ 0 and ≤ 1.

Parameters:

numberOfTrials - number of trials performed

numberOfSuccesses - number of successes observed

probability - assumed probability of a single trial under the null hypothesis

alternativeHypothesis - type of hypothesis being evaluated (one- or two-sided)

alpha - significance level of the test

Returns:

true if the null hypothesis can be rejected with confidence 1 - alpha

Throws:

NotPositiveException - if numberOfTrials or numberOfSuccesses is negative

OutOfRangeException - if probability is not between 0 and 1

MathIllegalArgumentException - if numberOfTrials < numberOfSuccesses or if alternateHypothesis is null.

See Also:

AlternativeHypothesis

binomialTest

public double binomialTest(int numberOfTrials,
                           int numberOfSuccesses,
                           double probability,
                           AlternativeHypothesis alternativeHypothesis)

Returns the observed significance level, or p-value, associated with a Binomial test.

The number returned is the smallest significance level at which one can reject the null hypothesis. The form of the hypothesis depends on alternativeHypothesis.

The p-Value represents the likelihood of getting a result at least as extreme as the sample, given the provided probability of success on a single trial. For single-sided tests, this value can be directly derived from the Binomial distribution. For the two-sided test, the implementation works as follows: we start by looking at the most extreme cases (0 success and n success where n is the number of trials from the sample) and determine their likelihood. The lower value is added to the p-Value (if both values are equal, both are added). Then we continue with the next extreme value, until we added the value for the actual observed sample.

Preconditions:

• Number of trials must be ≥ 0.
• Number of successes must be ≥ 0.
• Number of successes must be ≤ number of trials.
• Probability must be ≥ 0 and ≤ 1.

Parameters:

numberOfTrials - number of trials performed

numberOfSuccesses - number of successes observed

probability - assumed probability of a single trial under the null hypothesis

alternativeHypothesis - type of hypothesis being evaluated (one- or two-sided)

Returns:

p-value

Throws:

NotPositiveException - if numberOfTrials or numberOfSuccesses is negative

OutOfRangeException - if probability is not between 0 and 1

MathIllegalArgumentException - if numberOfTrials < numberOfSuccesses or if alternateHypothesis is null.

See Also:

AlternativeHypothesis