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BinomialTest Class

Binomial test.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.TestingHypothesisTestBinomialDistribution
    Accord.Statistics.TestingBinomialTest
      Accord.Statistics.TestingSignTest
      Accord.Statistics.TestingTwoSampleSignTest

Namespace:  Accord.Statistics.Testing
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.5.0
Syntax
[SerializableAttribute]
public class BinomialTest : HypothesisTest<BinomialDistribution>
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The BinomialTest type exposes the following members.

Constructors
Properties
  NameDescription
Public propertyCriticalValue
Gets the critical value for the current significance level.
(Inherited from HypothesisTestTDistribution.)
Public propertyHypothesis
Gets the alternative hypothesis under test. If the test is Significant, the null hypothesis can be rejected in favor of this alternative hypothesis.
Public propertyPValue
Gets the P-value associated with this test.
(Inherited from HypothesisTestTDistribution.)
Public propertySignificant
Gets whether the null hypothesis should be rejected.
(Inherited from HypothesisTestTDistribution.)
Public propertySize
Gets the significance level for the test. Default value is 0.05 (5%).
(Inherited from HypothesisTestTDistribution.)
Public propertyStatistic
Gets the test statistic.
(Inherited from HypothesisTestTDistribution.)
Public propertyStatisticDistribution
Gets the distribution associated with the test statistic.
(Inherited from HypothesisTestTDistribution.)
Public propertyTail
Gets the test type.
(Inherited from HypothesisTestTDistribution.)
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Methods
  NameDescription
Protected methodCompute
Computes the Binomial test.
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Protected methodOnSizeChanged
Called whenever the test significance level changes.
(Inherited from HypothesisTestTDistribution.)
Public methodPValueToStatistic
Converts a given p-value to a test statistic.
(Overrides HypothesisTestTDistributionPValueToStatistic(Double).)
Public methodStatisticToPValue
Converts a given test statistic to a p-value.
(Overrides HypothesisTestTDistributionStatisticToPValue(Double).)
Public methodToString
Converts the numeric P-Value of this test to its equivalent string representation.
(Inherited from HypothesisTestTDistribution.)
Public methodToString(String, IFormatProvider)
Converts the numeric P-Value of this test to its equivalent string representation.
(Inherited from HypothesisTestTDistribution.)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToTOverloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
Public Extension MethodToTOverloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by Matrix.)
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Remarks

In statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories. The most common use of the binomial test is in the case where the null hypothesis is that two categories are equally likely to occur (such as a coin toss).

When there are more than two categories, and an exact test is required, the multinomial test, based on the multinomial distribution, must be used instead of the binomial test.

References:

Examples

This is the second example from Wikipedia's page on hypothesis testing. In this example, a person is tested for clairvoyance (ability of gaining information about something through extra sensory perception; detecting something without using the known human senses.

// A person is shown the reverse of a playing card 25 times and is
// asked which of the four suits the card belongs to. Every time
// the person correctly guesses the suit of the card, we count this
// result as a correct answer. Let's suppose the person obtained 13
// correctly answers out of the 25 cards.

// Since each suit appears 1/4 of the time in the card deck, we 
// would assume the probability of producing a correct answer by
// chance alone would be of 1/4.

// And finally, we must consider we are interested in which the
// subject performs better than what would expected by chance. 
// In other words, that the person's probability of predicting
// a card is higher than the chance hypothesized value of 1/4.

BinomialTest test = new BinomialTest(
    successes: 13, trials: 25,
    hypothesizedProbability: 1.0 / 4.0,
    alternate: OneSampleHypothesis.ValueIsGreaterThanHypothesis);

Console.WriteLine("Test p-Value: " + test.PValue);     // ~ 0.003
Console.WriteLine("Significant? " + test.Significant); // True.
See Also