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


  • 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:
  • EqualVariancesFalsewhether the unknown population variances are assumed equal
    FullReportFalsewhether to include detailed information about a test
    KnownVarianceNonevariance of population
    SignificanceLevelNonesignificance level of the test
    TwoSidedFalsewhether to perform a two-sided test


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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: