## Hypotheses about the variance

Suppose we have a sample with variance and we assume that the true value of the sample variance is , then we can test the following hypotheses: H_{0} - ratio and the alternative hypothesis H_{A}:.

In practice, variance is often a measure of risk; therefore, while testing the hypothesis of the equality of variances, we evaluate how accurate is the risk degree is.

The verification of this hypothesis is performed with the help of the `VarianceTest`

function. This function can also check hypotheses on the equality of variances in several samples. For example, if one sample's variance is and the other's -, then the main hypothesis will be an equality check, . Mathematica conducts a series of tests to determine the probability of the hypothesis's truth.

Test's name |
Type of test |
Description |
---|---|---|

"BrownForsythe" |
Robust |
A robust Levene test |

"Conover" |
Symmetry |
This is based on squared ranks of the sample data |

"FisherRatio" |
Normality |
This is based on |

"Levene" |
robust... |