## Class BinomialTest

- java.lang.Object
- org.apache.commons.math3.stat.inference.BinomialTest

public class BinomialTestextends Object

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

- See Also:
- Binomial test (Wikipedia)

### Constructor Summary

Constructors Constructor and Description **BinomialTest**()

### Method Summary

Methods Modifier and Type Method and Description `double`

**binomialTest**(int numberOfTrials, int numberOfSuccesses, double probability, AlternativeHypothesis alternativeHypothesis)`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.

### 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`

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