com.imsl.stat
Class NormOneSample

java.lang.Object
  com.imsl.stat.NormOneSample

All Implemented Interfaces:

Serializable, Cloneable

public class NormOneSample
extends Object
implements Serializable, Cloneable

Computes statistics for mean and variance inferences using a sample from a normal population.

The statistics for mean and variance inferences are computed by using a sample from a normal population, including methods for the confidence intervals and tests for both mean and variance. The definitions of mean and variance are given below. The summation in each case is over the set of valid observations, based on the presence of missing values in the data.

Method getMean, returns value

Method getStandardDeviation, returns value

The method getTTestStat returns the t statistic for the two-sided test concerning the population mean which is given by

where s and are given above. This quantity has a T distribution with n - 1 degrees of freedom. The method getTTestDF returns the degree of freedom.

The method getChiSquaredTestStat returns the chi-squared statistic for the two-sided test concerning the population variance which is given by

where s is given above. This quantity has a distribution with n - 1 degrees of freedom. The method getChiSquaredTestDF returns the degrees of freedom.

See Also:

Example, Serialized Form

Constructor Summary

NormOneSample(double[] x)
Constructor to compute statistics for mean and variance inferences using a sample from a normal population.

Method Summary

double	getChiSquaredTest() Returns the test statistic associated with the chi-squared test for variances.
int	getChiSquaredTestDF() Returns the degrees of freedom associated with the chi-squared test for variances.
double	getChiSquaredTestP() Returns the probability of a larger chi-squared associated with the chi-squared test for variances.
double	getLowerCIMean() Returns the lower confidence limit for the mean.
double	getLowerCIVariance() Returns the lower confidence limits for the variance.
double	getMean() Returns the mean of the sample.
double	getStdDev() Returns the standard deviation of the sample.
double	getTTest() Returns the test statistic associated with the t test.
int	getTTestDF() Returns the degrees of freedom associated with the t test for the mean.
double	getTTestP() Returns the probability associated with the t test of a larger t in absolute value.
double	getUpperCIMean() Returns the upper confidence limit for the mean.
double	getUpperCIVariance() Returns the upper confidence limits for the variance.
void	setChiSquaredTestNull(double chiSqrTestNull) Sets the null hypothesis value for the chi-squared test.
void	setConfidenceMean(double confidenceMean) Sets the confidence level (in percent) for a two-sided interval estimate of the mean.
void	setConfidenceVariance(double confidenceVariance) Sets the confidence level (in percent) for two-sided interval estimate of the variances.
void	setTTestNull(double meanHypothesis) Sets the Null hypothesis value for t test for the mean.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NormOneSample

public NormOneSample(double[] x)

Constructor to compute statistics for mean and variance inferences using a sample from a normal population.

Parameters:

x - is a one-dimension double array containing the observations.

Method Detail

getChiSquaredTest

public double getChiSquaredTest()

Returns the test statistic associated with the chi-squared test for variances. The chi-squared test is a test of the hypothesis where is the null hypothesis value as described in setChiSquaredTestNull.

Returns:

a double containing the test statistic for the chi-squared test.

getChiSquaredTestDF

public int getChiSquaredTestDF()

Returns the degrees of freedom associated with the chi-squared test for variances. The chi-squared test is a test of the hypothesis where is the null hypothesis value as described in setChiSquaredTestNull.

Returns:

an int the degrees of freedom for the chi-squared test.

getChiSquaredTestP

public double getChiSquaredTestP()

Returns the probability of a larger chi-squared associated with the chi-squared test for variances. The chi-squared test is a test of the hypothesis where is the null hypothesis value as described in setChiSquaredTestNull.

Returns:

a double containing the probability of a larger chi-squared for the chi-squared test for variances.

getLowerCIMean

public double getLowerCIMean()

Returns the lower confidence limit for the mean.

Returns:

a double containing the lower confidence limit for the mean.

getLowerCIVariance

public double getLowerCIVariance()

Returns the lower confidence limits for the variance.

Returns:

a double containing the lower confidence limits for the variance.

getMean

public double getMean()

Returns the mean of the sample.

Returns:

a double containing the mean.

getStdDev

public double getStdDev()

Returns the standard deviation of the sample.

Returns:

a double containing the standard deviation of the sample.

getTTest

public double getTTest()

Returns the test statistic associated with the t test. The t test is a test, against a two-sided alternative, of the null hypothesis value described in setTTestNull.

Returns:

a double containing the test statistic for the t test.

getTTestDF

public int getTTestDF()

Returns the degrees of freedom associated with the t test for the mean. The t test is a test, against a two-sided alternative, of the null hypothesis value described in setTTestNull.

Returns:

an int containing the degrees of freedom for the t test.

getTTestP

public double getTTestP()

Returns the probability associated with the t test of a larger t in absolute value. The t test is a test, against a two-sided alternative, of the null hypothesis value described in setTTestNull.

Returns:

a double containing the probability for the t test.

getUpperCIMean

public double getUpperCIMean()

Returns the upper confidence limit for the mean.

Returns:

a double containing the upper confidence limit for the mean.

getUpperCIVariance

public double getUpperCIVariance()

Returns the upper confidence limits for the variance.

Returns:

a double the upper confidence limits for the variance.

setChiSquaredTestNull

public void setChiSquaredTestNull(double chiSqrTestNull)

Sets the null hypothesis value for the chi-squared test. The default is 1.0.

Parameters:

chiSqrTestNull - double containing the null hypothesis value for the chi-squared test.

setConfidenceMean

public void setConfidenceMean(double confidenceMean)

Sets the confidence level (in percent) for a two-sided interval estimate of the mean.

Parameters:

confidenceMean - double containing the confidence level of the mean. confidenceMean must be between 0.0 and 1.0 and is often 0.90, 0.95 or 0.99. For a one-sided confidence interval with confidence level c less than 50 percent, set confidenceMean =1.0- 2.0*(c/100). This effectively gives the one-sided confidence interval for both c% and (100-c)%. For example, for a one-sided t-test with confidence level of 40, set confidenceMean=.2 . This means that 40% of the distribution is lower than confidence limit for the mean (see getLowerCIMean) and 40% of the distribution is greater than the upper confidence limit for the mean (see getUpperCIMean). It also means that 60% of the distribution is greater than the lower confidence limit for the mean and 60% is lower than upper confidence limit for the mean. If the confidence mean is not specified, a 95-percent confidence interval is computed.

setConfidenceVariance

public void setConfidenceVariance(double confidenceVariance)

Sets the confidence level (in percent) for two-sided interval estimate of the variances. Argument confidenceVariance must be between 0.0 and 1.0 and is often 0.90, 0.95 or 0.99. For a one-sided confidence interval with confidence level c (at least 50 percent), set confidenceVariance=1.0-2.0 * (1.0 - c). If the confidence mean is not specified, a 95-percent confidence interval is computed.

Parameters:

confidenceVariance - double containing the confidence level of the variance.

setTTestNull

public void setTTestNull(double meanHypothesis)

Sets the Null hypothesis value for t test for the mean. meanHypothesis=0.0 by default.

Parameters:

meanHypothesis - double containing the hypothesis value.