NMath Stats User's Guide

13.2 Significance of Parameters (.NET, C#, CSharp, Visual Basic, VB.NET)

Instances of class GoodnessOfFitParameter test statistical hypothesis about individual parameters in a least squares model-fit.

Creating Goodness of Fit Parameter Objects

You can get an array of test objects for all parameters in a GoodnessOfFit using the Parameters property:

GoodnessOfFitParameter[] params = gof.Parameters; 

Properties of Goodness of Fit Parameters

Class GoodnessOfFitParameter provides the following properties:

• Index gets the index of the parameter in the overall model.
• Value gets the value of the parameter.
• StandardError gets the standard error of the parameter.
• DegreesOfFreedom gets the degrees of freedom of the parameter.

Hypothesis Tests

Class GoodnessOfFitParameter provides the following methods for testing statistical hypotheses regarding parameter values:

• TStatisticPValue() returns the p-value for a two-sided t test with the null hypothesis that the parameter is equal to a given test value, versus the alternative hypothesis that it is not.
• TStatistic() returns the value of the t statistic for the null hypothesis that the parameter value is equal to a given test value.
• TStatisticCriticalValue() gets the critical value for the t-statistic for a given alpha level.
• ConfidenceInterval() returns a confidence interval for the parameter for a given alpha level.

For example, this code tests whether a parameter in a model is significantly different than zero:

double tstat = param.TStatistic( 0.0 );
double pValue = param.TStatisticPValue( 0.0 );
double criticalValue = param.TStatisticCriticalValue( 0.05 );
Interval confidenceInterval = param.ConfidenceInterval( 0.05 );

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