Test some data for normality:
The
-values for the normally distributed data are typically large:
The
-values for data that is not normally distributed are typically small:
Set the third argument to
Automatic to apply a generally powerful and appropriate test:
The property
can be used to determine which test was chosen:
Test whether data fits a particular distribution:
There is insufficient evidence to reject a good fit to a
WeibullDistribution
:
Test for goodness of fit to a derived distribution:
The
-value is large for the mixture data compared to data not drawn from the mixture:
Test for goodness of fit to a formula-based distribution:
Unspecified parameters will be estimated from the data:
The
-value is dependent on which parameters were estimated:
Test some data for multivariate normality:
The
-values for normally distributed data are typically large compared to non-normal data:
Test some data for goodness of fit to a particular multivariate distribution:
Compare the distributions of two datasets:
The sample sizes need not be equal:
Compare the distributions of two multivariate datasets:
The
-values for equally distributed data are large compared to unequally distributed data:
Perform a particular goodness-of-fit test:
Any number of tests can be performed simultaneously:
Perform all tests, appropriate to the data and distribution, simultaneously:
Use the property
to identify which tests were used:
Create a
HypothesisTestData object for repeated property extraction:
The properties available for extraction:
Extract some properties from a
HypothesisTestData object:
The
-value and test statistic from a Cramér-von Mises test:
Extract any number of properties simultaneously:
The results from the Anderson-Darling
-value and test statistic:
Obtain the fitted distribution when parameters have been unspecified:
Extract the parameters from the fitted distribution:
Plot the PDF of the fitted distribution against the data:
Confirm the fit with a goodness-of-fit test:
The test distribution is returned when the parameters have been specified:
Visually compare the data to the fitted distribution:
Tabulate the results from a selection of tests:
A full table of all appropriate test results:
A table of selected test results:
Retrieve the entries from a test table for customized reporting:
The
-values are above 0.05 so there is not enough evidence to reject normality at that level:
Tabulate
-values for a test or group of tests:
The
-value from the table:
A table of
-values from all appropriate tests:
A table of
-values from a subset of tests:
Report the test statistic from a test or group of tests:
The test statistic from the table:
A table of test statistics from all appropriate tests:
.
that data was drawn from a population with distribution dist and alternative hypothesis 
that it was not.
-value is returned. 
-value suggests that it is unlikely that the data came from dist.
or multivariate 
.
reports the 
-value according to 
.
of the test distribution dist and the empirical CDF 
of the data as well as their difference 
and 
=Expectation[d(x), ...]. The CDFs 
and 
should be the same under the null hypothesis 
. 
returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"]. 
can be used to directly give the value of 
.
-values
-values
-values
-values and test statistics
-values
is chosen such that 
is rejected only if 
. The value of 
used for the 
and 
properties is controlled by the SignificanceLevel option. By default 
is set to 0.05.
, 
datasets of the same length as the input 
are generated under 
using the fitted distribution. The EmpiricalDistribution from DistributionFitTest
is then used to estimate the 
-value.
-value with increasing samples:
-value:
:
:
-value agrees with the Monte Carlo estimate:
:
test are useful for testing uniformity on a circle:
-value:
-value from an Anderson-Darling test:
-value returned by DistributionFitTest:
, the test size is 0.05, and the sample size is 35:
-value suggests the expected proportion of false positives (type I errors):
about 5% of the time:
is not rejected, given it is false:
when it is false:
test has the lowest power:
test requires large sample sizes to have high power:
-values under 
:
-values:
-values:
-value:
-values:
-value:
test is the only test that applies to discrete distributions:
EXAMPLES
Basic Examples 
Scope 
