HypothesisTesting`
HypothesisTesting`

# VarianceRatioTest

VarianceRatioTest[list1,list2,r]

performs a test with null hypothesis .

# Details and Options

• To use VarianceRatioTest, you first need to load the Hypothesis Testing Package using Needs["HypothesisTesting`"].
• VarianceRatioTest[list1,list2,r] gives a value for the test that the ratio of the variances and of the populations from which list1 and list2 were sampled is significantly different from r.
• VarianceRatioTest uses the test statistic Variance[list1]/Variance[list2]/r.
• VarianceRatioTest is based on an F-ratio distribution with Length[list1]-1 and Length[list2]-1 degrees of freedom.
• The following options can be given:
•  FullReport False whether to include detailed information about a test SignificanceLevel None significance level of the test TwoSided False whether to perform a two-sided test
• With the option , VarianceRatioTest also returns the ratio of sample variances, the test statistic, and the distribution used to generate the -value.

# Examples

open allclose all

## Basic Examples(1)

A test of the ratio of population variances against 2:

## Options(3)

### FullReport(1)

A full report for a variance ratio test:

### SignificanceLevel(1)

A test at significance level .01:

### TwoSided(1)

A twosided variance ratio test:

Wolfram Research (2007), VarianceRatioTest, Wolfram Language function, https://reference.wolfram.com/language/HypothesisTesting/ref/VarianceRatioTest.html.

#### Text

Wolfram Research (2007), VarianceRatioTest, Wolfram Language function, https://reference.wolfram.com/language/HypothesisTesting/ref/VarianceRatioTest.html.

#### CMS

Wolfram Language. 2007. "VarianceRatioTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/HypothesisTesting/ref/VarianceRatioTest.html.

#### APA

Wolfram Language. (2007). VarianceRatioTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/HypothesisTesting/ref/VarianceRatioTest.html

#### BibTeX

@misc{reference.wolfram_2024_varianceratiotest, author="Wolfram Research", title="{VarianceRatioTest}", year="2007", howpublished="\url{https://reference.wolfram.com/language/HypothesisTesting/ref/VarianceRatioTest.html}", note=[Accessed: 24-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_varianceratiotest, organization={Wolfram Research}, title={VarianceRatioTest}, year={2007}, url={https://reference.wolfram.com/language/HypothesisTesting/ref/VarianceRatioTest.html}, note=[Accessed: 24-July-2024 ]}