Tests represented on this page are used to check hypotheses about random variables dispersion.

This test is used to check hypotheses about the fact that dispersion of random variable X represented by sample *x _{S }* equals given

During its work, the test calculates the c-statistic:

If X has a normal distribution, the c-statistic will have a chi-square distribution with N-1 degrees of freedom. To define the significance level which corresponds to the value of c-statistic high-precision chi-square distribution approximation is used. Test returns three p-values:

- p-value for two-tailed test (null hypothesis - the dispersion is equal to the given number)
- p-value for left-tailed test (null hypothesis - the dispersion is greater than or equal to the given number)
- p-value for right-tailed test (null hypothesis - the dispersion is less than or equal to the given number)

This test checks hypotheses about the fact that the dispersions of two random variables X and Y which are represented by samples xS and yS are equal. The test works correctly under the following conditions:

- both random variables have a normal distribution
- the samples are independent

During its work, the test calculates the F-statistic:

If X and Y have a normal distribution, the F-statistic will have F-distribution with NX -1 and NY -1 degrees of freedom. To define the significance level which corresponds to the value of F-statistic high-precision, F-distribution approximation is used.

Test returns three p-values:

- p-value for two-tailed test (null hypothesis - the dispersions are equal)
- p-value for left-tailed test (null hypothesis - the dispersion of the first sample is greater than or equal to the dispersion of the second sample)
- p-value for right-tailed test (null hypothesis - the dispersion of the first sample is less than or equal to the dispersion of the second sample)

C++ | `variancetests` subpackage | |

C# | `variancetests` subpackage |

*This article is intended for personal use only.*

C# source.

C++ source.

C++ source. MPFR/GMP is used.

GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.

FreePascal version.

Delphi version.

VB.NET version.

VBA version.

Python version (CPython and IronPython are supported).

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