**5.1****
****Common Interface** (.NET, C#, CSharp, VB, Visual Basic, F#)

All hypothesis test classes share substantially the same interface. Once you learn how to use one test, it's easy to use any of the others.

All hypothesis test classes have static DefaultAlpha properties that get and set the default alpha level associated with tests of that type. The default value is 0.01. For instance:

Code Example – C# hypothesis tests

var test1 = new OneSampleTTest(); // test1.Alpha == 0.01 OneSampleTTest.DefaultAlpha = 0.05; var test2 = new OneSampleTTest(); // test2.Alpha == 0.05

Similarly, all hypothesis test classes have static
DefaultType properties that get and set
the default form of the alternative hypothesis. The form is specified
using the **HypothesisType** enumeration,
with the following enumerated values:

● Left indicates a one-sided form to the left, .

● Right indicates a one-sided form to the right, .

● TwoSided indicates a two-sided form, .

The default value for all test classes is HypothesisType.TwoSided. For example:

Code Example – C# hypothesis tests

var test1 = new OneSampleTTest(); // test1.Type == HypothesisType.TwoSided OneSampleTTest.DefaultType = HypothesisType.Left; var test2 = new OneSampleTTest(); // test2.Type == HypothesisType.Left

**Creating Hypothesis Test Objects**

All hypothesis test classes provide two paths for constructing instances of that type:

● A *parameter-based* method, in which all necessary
sample and population parameters are explicitly specified.

● A *data-based* method, in which sample parameters
are computed from supplied sample data.

**NOTE—****In
the data-based method, once sample parameters have been computed from
the given data, the data is discarded, and cannot be recovered from the
test object.**

For example, a one-sample z-test compares a single
sample mean to an expected mean from a normal distribution with known
standard deviation. This code constructs a **OneSampleZTest**
object by explicitly specifying a sample mean, sample size, population
mean, and population standard deviation:

Code Example – C# hypothesis tests

double xbar = 112.8; int n = 9; double mu0 = 100; double sigma = 15; var test = new OneSampleZTest( xbar, n, mu0, sigma );

This code constructs a **OneSampleZTest**
object by supplying a vector of sample data, and the necessary population
parameters:

Code Example – C# hypothesis tests

var data = new DoubleVector( "[ 116 110 111 113 112 113 111 109 121 ]" ); double mu0 = 100; double sigma = 15; var test = new OneSampleZTest( data, mu0, sigma );

In this case, the sample mean and sample size are calculated from the given data. The data-based method supports sample data in vectors, arrays, and data frame columns.

In both the parameter-based method and the data-based method, the alpha level for the hypothesis test is set to the current value specified by the static DefaultAlpha property, and the form of the hypothesis test is set to the current DefaultType, as described above.

Constructors are also provided for all test classes that enable you to set the alpha level and hypothesis type to non-default values. For example:

Code Example – C# hypothesis tests

var test = new OneSampleZTest( data, mu0, sigma, 0.05, HypothesisType.Left );

**Properties of Hypothesis Test Objects**

All hypothesis test classes provide the following read-only properties:

● Distribution gets the distribution of the test statistic associated with the hypothesis test.

● Statistic gets the value of the test statistic associated with this hypothesis test.

● P gets the *p*-value
associated with the test statistic.

● Reject tests whether the null hypothesis can be rejected, using the current hypothesis type and alpha level.

● LeftCriticalValue gets the one-sided to the left critical value based on the current probability distribution and alpha level.

● RightCriticalValue gets the one-sided to the right critical value based on the current probability distribution and alpha level.

● LeftProbability gets the area under the probability distribution to the left of the test statistic.

● RightProbability gets the area under the probability distribution to the right of the test statistic.

● LowerConfidenceLimit gets the lower confidence limit for the true mean.

● UpperConfidenceLimit gets the upper confidence limit for the true mean.

● SEM gets the standard error of the mean.

The following read-write properties are also provided:

● Alpha gets and sets the alpha level associated with the hypothesis test.

● Type gets and sets the form of the alternative hypothesis associated with the hypothesis test.

Additionally, each hypothesis test provides properties
for accessing the specific sample and population parameters that define
the test. For example, a **OneSampleZTest**
has additional properties for accessing the sample mean, Xbar, the sample size, N,
the population mean, Mu0, and the population
standard deviation, Sigma.

**Modifying Hypothesis Test Objects**

All hypothesis test classes provide Update()
methods for modifying a test with new sample parameters or sample data,
and new population parameters. For example, if test
is a **TwoSampleFTest** instance, this
code updates the test with two new samples, taken from two columns in
a data frame df:

Code Example – C# hypothesis tests

test.Update( df[3], df[7] );

All hypothesis test classes provide a ToString() method that returns a formatted string representation of the test results. For instance:

Code Example – C# hypothesis tests

var data1 = new DoubleVector( "9.21 11.51 12.79 11.85 9.97 8.79 9.69 9.68 9.19" ); var data2 = new DoubleVector( "7.53 7.48 8.08 8.09 10.15 8.40 10.88 6.13 7.90 7.05 7.48 7.58 8.11" ); var test = new TwoSampleFTest( data1, data2, 0.05, HypothesisType.TwoSided ); Console.WriteLine( test.ToString() );

The output is:

Two Sample F Test ----------------- Sample Sizes = 9 and 13 Standard Deviations = 1.39787139767736 and 1.23808008936914 Variances = 1.95404444444444 and 1.53284230769231 Ratio of Variances = 1.27478504125206 Computed F statistic: 1.27478504125206, num df = 8, denom df = 12 Hypothesis type: two-sided Null hypothesis: true ratio of variances = 1 Alt hypothesis: true ratio of variances != 1 P-value: 0.679745985376403 RETAIN the null hypothesis for alpha = 0.05 0.95 confidence interval: 0.363002872041806 5.3536732579205