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MeanDifferenceTest

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

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Basic Examples (1)

Wolfram Language code: Needs["HypothesisTesting`"]

A test of the difference of population means against 0:

Wolfram Language code: MeanDifferenceTest[{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}, 0]

Options (5)

EqualVariances (1)

Wolfram Language code: Needs["HypothesisTesting`"]

A test assuming equal variances:

Wolfram Language code: MeanDifferenceTest[{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}, 0, EqualVariances -> True]

FullReport (1)

Wolfram Language code: Needs["HypothesisTesting`"]

A full report for a mean difference test:

Wolfram Language code: MeanDifferenceTest[{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}, 0, FullReport -> True]

KnownVariance (1)

Wolfram Language code: Needs["HypothesisTesting`"]

A test assuming the population variances are 1 and 3:

Wolfram Language code: MeanDifferenceTest[{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}, 0, KnownVariance -> {1, 3}]

SignificanceLevel (1)

Wolfram Language code: Needs["HypothesisTesting`"]

A test at significance level .01:

Wolfram Language code: MeanDifferenceTest[{1,2,4,6,3},{4,10,6,8,5,8},0,SignificanceLevel->.01]

TwoSided (1)

Wolfram Language code: Needs["HypothesisTesting`"]

A two‐sided mean difference test:

Wolfram Language code: MeanDifferenceTest[{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}, 0, TwoSided -> True]

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