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

One sample chi-square test

This test is used to check hypotheses about the fact that dispersion of random variable X represented by sample x_S  equals given σ ².

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)

Two-sample F-test

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)

Links

1. 'Hypothesis testing', Wikipedia
2. 'P-value', Wikipedia

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C#

C# 1.0 source.
variancetests.csharp.zip - F-test and chi-square test

C++

C++ source.
variancetests.cpp.zip - F-test and chi-square test
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
variancetests.delphi.zip - F-test and chi-square test

Visual Basic 6

Visual Basic 6 source.
variancetests.vb6.zip - F-test and chi-square test

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
variancetests.zonnon.zip - F-test and chi-square test