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

Class BinomialTest

java.lang.Object
org.apache.commons.math4.stat.inference.BinomialTest
public class BinomialTest
extends java.lang.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 Details

  • Method Details

    • 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