BUILT-IN MATHEMATICA SYMBOL

# PairedTTest

PairedTTest[data]
tests whether the mean of data is zero.

PairedTTest[{data1, data2}]
tests whether the mean of is zero.

PairedTTest[dspec, 0]
tests a location measure against .

PairedTTest[dspec, 0, "property"]
returns the value of .

## Details and OptionsDetails and Options

• PairedTTest performs a hypothesis test on data with null hypothesis that the true population mean is some value , and alternative hypothesis that .
• Given and , PairedTTest performs a test on the paired differences of the two datasets.
• By default a probability value or -value is returned.
• A small -value suggests that it is unlikely that is true.
• The data in dspec can be univariate or multivariate .
• If two samples are given, they must be of equal length.
• The argument can be a real number or a real vector with length equal to the dimension of the data.
• PairedTTest[dspec, 0, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• PairedTTest[dspec, 0, "property"] can be used to directly give the value of .
• Properties related to the reporting of test results include:
•  "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
• PairedTTest is more powerful than the TTest when samples are matched.
• For univariate samples PairedTTest performs the Student -test for matched pairs. The test statistic is assumed to follow a StudentTDistribution.
• For multivariate samples, PairedTTest performs Hotelling's test for matched pairs. The test statistic is assumed to follow a HotellingTSquareDistribution.
• The following options can be used:
•  AlternativeHypothesis "Unequal" the inequality for the alternative hypothesis SignificanceLevel 0.05 cutoff for diagnostics and reporting VerifyTestAssumptions Automatic what assumptions to verify
• For the PairedTTest, 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 PairedTTest include:
•  "Normality" verify that all data is normally distributed

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Test whether the mean of a population is zero:

 Out[2]=

The full test table:

 Out[3]=

Test whether the means of two dependent populations differ:

The mean of the differences:

 Out[2]=
 Out[3]=

At the level the mean of the differenced data is not significantly different from 0:

 Out[4]=

Compare the locations of dependent multivariate populations:

The mean of the differences:

 Out[2]=
 Out[3]=

At the level the mean of the differenced data is not significantly different from 0:

 Out[4]=