# 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:

• 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)

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