HypothesisTesting`
HypothesisTesting`

# MeanDifferenceTest

MeanDifferenceTest[list1,list2,Δμ0]

performs a test with null hypothesis μ1-μ2=Δμ0.

# Details and Options

• To use MeanDifferenceTest, you first need to load the Hypothesis Testing Package using Needs["HypothesisTesting`"].
• MeanDifferenceTest[list1,list2, Δμ0] gives a value for the test that the difference between the means μ1 and μ2 of the populations from which list1 and list2 were sampled is significantly different from Δμ0.
• MeanDifferenceTest is based on a normal distribution if the population variances are assumed known.
• If the variances for the two populations are assumed equal and unknown, the test is based on Student's distribution with Length[list1]+Length[list2]-2 degrees of freedom.
• If the population variances are not assumed known and not assumed equal, Welch's approximation for the degrees of freedom is used.
• The following options can be given:
•  EqualVariances False whether the unknown population variances are assumed equal FullReport False whether to include detailed information about a test KnownVariance None variance of population SignificanceLevel None significance level of the test TwoSided False whether to perform a two-sided test

# Examples

open allclose all

## Basic Examples(1)

A test of the difference of population means against 0:

## Options(5)

### EqualVariances(1)

A test assuming equal variances:

### FullReport(1)

A full report for a mean difference test:

### KnownVariance(1)

A test assuming the population variances are 1 and 3:

### SignificanceLevel(1)

A test at significance level .01:

### TwoSided(1)

A twosided mean difference test:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_meandifferencetest, author="Wolfram Research", title="{MeanDifferenceTest}", year="2007", howpublished="\url{https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceTest.html}", note=[Accessed: 17-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_meandifferencetest, organization={Wolfram Research}, title={MeanDifferenceTest}, year={2007}, url={https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceTest.html}, note=[Accessed: 17-June-2024 ]}