F-test and chi-square test

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 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:

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:

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:

Links

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

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