public class BinomialTest extends Object
Exact test for the statistical significance of deviations from a theoretically expected distribution of observations into two categories.
Constructor and Description |
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BinomialTest() |
Modifier and Type | Method and Description |
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double |
binomialTest(int numberOfTrials,
int numberOfSuccesses,
double probability,
AlternativeHypothesis alternativeHypothesis)
Returns the observed significance level, or
p-value,
associated with a Binomial test.
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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.
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public boolean binomialTest(int numberOfTrials, int numberOfSuccesses, double probability, AlternativeHypothesis alternativeHypothesis, double alpha)
Preconditions:
numberOfTrials
- number of trials performednumberOfSuccesses
- number of successes observedprobability
- assumed probability of a single trial under the null hypothesisalternativeHypothesis
- type of hypothesis being evaluated (one- or two-sided)alpha
- significance level of the test1 - alpha
NotPositiveException
- if numberOfTrials
or numberOfSuccesses
is negativeOutOfRangeException
- if probability
is not between 0 and 1MathIllegalArgumentException
- if numberOfTrials
< numberOfSuccesses
or
if alternateHypothesis
is null.AlternativeHypothesis
public double binomialTest(int numberOfTrials, int numberOfSuccesses, double probability, AlternativeHypothesis alternativeHypothesis)
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:
numberOfTrials
- number of trials performednumberOfSuccesses
- number of successes observedprobability
- assumed probability of a single trial under the null hypothesisalternativeHypothesis
- type of hypothesis being evaluated (one- or two-sided)NotPositiveException
- if numberOfTrials
or numberOfSuccesses
is negativeOutOfRangeException
- if probability
is not between 0 and 1MathIllegalArgumentException
- if numberOfTrials
< numberOfSuccesses
or
if alternateHypothesis
is null.AlternativeHypothesis
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