BUILT-IN MATHEMATICA SYMBOL
TTest
TTest[data]
tests whether the mean of data is zero.
TTest[{data1, data2}]
tests whether the means of 
and 
are equal.
TTest[dspec, 
0]
tests the mean against 
.
TTest[dspec, 0, "property"]
returns the value of 
.
- TTest performs a hypothesis test on data with null hypothesis
that the true population mean is some value 
, and alternative hypothesis 
that 
.
- Given
and 
, TTest tests 
that 
against 
that 
.
- 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 
.
- The argument
can be a real number or a real vector with length equal to the dimension of the data.
- TTest assumes that the data is normally distributed but is fairly robust to this assumption. TTest also assumes that the samples are independent in the two sample case.
- TTest[dspec, 0, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
- TTest[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 |
- For univariate samples, TTest performs a Student
test. The test statistic is assumed to follow a StudentTDistribution[df].
- For multivariate samples, TTest performs Hotelling's
test. The test statistic is assumed to follow a HotellingTSquareDistribution[p, df] where p is the dimension of data.
- The degrees of freedom df, used to specify the distribution of the test statistic, depend on the sample size, number of samples, and in the case of two univariate samples, the results of a test for equal variances.
- The following options can be used:
-
- For the TTest, 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 TTest include:
-
| "Normality" | verify that all data is normally distributed |
| "EqualVariance" | verify that  and  have equal variance |
New in 8
is significantly different from 2:
is not significantly different from 
:
