Meta.Numerics Library

## SampleStudentTTest Method (Sample, Sample) |

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

Syntax

- 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.

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

Exception | Condition |
---|---|

ArgumentNullException | a or b is null. |

InsufficientDataException | a 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