BUILTIN MATHEMATICA SYMBOL
LocationEquivalenceTest
 LocationEquivalenceTest performs a hypothesis test on the with null hypothesis that the true location parameters of the populations are equal , and alternative hypothesis that at least one is different.
 By default a probability value or value is returned.
 A small value suggests that it is unlikely that is true.
 The must be univariate .
 LocationEquivalenceTest[{data_{1}, ...}] will choose the most powerful test that applies to the data.
 LocationEquivalenceTest[{data_{1}, ...}, All] will choose all tests that apply to the data.
 LocationEquivalenceTest[{data_{1}, ...}, "test"] reports the value according to .
 Meanbased tests assume that the are normally distributed. The medianbased KruskalWallis test assumes that are symmetric about a common median. The complete block and Friedman rank tests assume that the data is in randomized complete blocks. All of the tests require the to have equal variances.
 The following tests can be used:

 "CompleteBlockF"  normality, blocked  mean test for complete block design 
 "FriedmanRank"  blocked  median test for complete block design 
 "KruskalWallis"  symmetry  median test for two or more samples 
 "KSampleT"  normality  mean test for two or more samples 
 The complete block test effectively performs oneway analysis of variance for randomized complete block design.
 The Friedman rank test ranks observations across rows and sums the ranks along columns in the data to arrive at the test statistic. The statistic is corrected for ties.
 The KruskalWallis test effectively performs a oneway analysis of variance on the ranks of the data. The test statistic is corrected for ties.
 The sample test is equivalent to a oneway analysis of variance of the data.
 LocationEquivalenceTest[{data_{1}, ...}, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
 LocationEquivalenceTest[{data_{1}, ...}, "property"] can be used to directly give the value of .
 Properties related to the reporting of test results include:

 "AllTests"  list of all applicable tests 
 "AutomaticTest"  test chosen if Automatic is used 
 "DegreesOfFreedom"  the degrees of freedom used in a test 
 "PValue"  list of values 
 "PValueTable"  formatted table of values 
 "ShortTestConclusion"  a short description of the conclusion of a test 
 "TestConclusion"  a description of the conclusion of a test 
 "TestData"  list of pairs of test statistics and values 
 "TestDataTable"  formatted table of values and test statistics 
 "TestStatistic"  list of test statistics 
 "TestStatisticTable"  formatted table of test statistics 
 The following options can be given:

 For tests of location, a cutoff is chosen such that is rejected only if . The value of used for the and properties is controlled by the SignificanceLevel option. This value is also used in diagnostic tests of assumptions, including tests for normality, equal variance, and symmetry. By default is set to .
 Named settings for VerifyTestAssumptions in LocationEquivalenceTest include:

 "Normality"  verify that all data is normally distributed 
 "EqualVariance"  verify that the have equal variances 
 "Symmetry"  verify symmetry about a common median 
New in 8