# Chapter 3

# Tests on the variance

This chapter contains statistical tests on the variance of normal populations. In the one-sample case it is of interest whether the variance of a single population differs from some pre-specified value, where the mean value of the underlying Gaussian distribution may be known or unknown. SAS and R do not provide the user with ready to use procedures or functions for the resulting -tests. For the two-sample cases it must be distinguished between independent and dependent samples. In the former case an F-test and in the latter case a t-test is appropriate. The SAS procedure proc ttest provides a way to calculate the test for the two-sided hypothesis. We additionally show how the test can be performed for the one-sided hypothesis. In R the function var.test calculates the test for all hypotheses. In SAS and R there is no convenient way to calculate the t-test for dependent samples and we provide code for it. For k-sample variance tests (Levene test, Bartlett test) please refer to Chapter 17 which covers ANOVA tests.

# 3.1 One-sample tests

This section deals with the question, if the variance differs from a predefined value.

## 3.1.1 -test on the variance (mean known)

**Description:** |
Tests if a population variance differs from a specific value . |

**Assumptions: ...** |