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SampleStudentTTest Method (Sample, Sample)

Tests whether one sample mean is compatible with another sample mean.

Namespace:  Meta.Numerics.Statistics
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 4.0.5.0 (4.0.5.0)
Syntax
public static TestResult StudentTTest(
	Sample a,
	Sample b
)

Parameters

a
Type: Meta.Numerics.StatisticsSample
The first sample, which must contain at least two entries.
b
Type: Meta.Numerics.StatisticsSample
The second sample, which must contain at least two entries.

Return Value

Type: TestResult
The result of the test. The statistic is the Student's t and the probability is the chance of obtaining such an extreme value of t if the two samples are drawn from the same distribution.
Exceptions
ExceptionCondition
ArgumentNullExceptiona or b is null.
InsufficientDataExceptiona or b contains less than two values.
Remarks

Given two samples, a back-of-the-envelope way to determine whether their means differ in a statistically significant way is to compare their PopulationMean values. If their error bars overlap, they are probably statistically compatible; if they do not, the difference in means is probably statistically significant. Student's t-test is a way to refine this back-of-the-envelope procedure into a statistical test that can determine exactly how likely a given seperation of means is under the null hypothesis that the two samples are drawn from the same distribution.

The t-statistic is proportional to the mean of a minus the mean of b, so t > 0 indicates that a has a greater mean.

Student's t-test was one of the first statistical tests. It was described by William Sealy Gosset, a chemist who worked for the Guiness brewing company. Since Guiness was concerned that other breweries might take advantage of a technique published by one of its chemists, Gosset published his work under the pseudonym Student.

See Also