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