Package 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

$$\bar x = \frac{{\sum {x_i } }}{n}$$

$$\Delta _s^d Z_t$$

Method getStandardDeviation, returns value

$$s = \sqrt {\frac{{\sum {\left( {x_i - \bar x} \right)^2 } }}{{n - 1}}}$$

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

$$t = \frac{{\bar x - \mu _0 }}{{s/\sqrt n }}$$

where s and \(\bar x\) 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

$$\chi ^2 = \frac{{\left( {n - 1} \right)s^2 }}{{\sigma _0^2 }}$$

where s is given above. This quantity has a \(\chi ^2\) distribution with n - 1 degrees of freedom. The method getChiSquaredTestDF returns the degrees of freedom.

See Also:

  • Constructor Summary

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

  • Method Summary

    Modifier and Type
    Method
    Description
    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 Details

    • 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 Details

    • getMean

      public double getMean()
      Returns the mean of the sample.
      Returns:
      a double containing the mean.

    • 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 (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.

    • getLowerCIMean

      public double getLowerCIMean()
      Returns the lower confidence limit for the mean.
      Returns:
      a double containing the lower confidence limit for the mean.

    • getUpperCIMean

      public double getUpperCIMean()
      Returns the upper confidence limit for the mean.
      Returns:
      a double containing the upper confidence limit for the mean.

    • getStdDev

      public double getStdDev()
      Returns the standard deviation of the sample.
      Returns:
      a double containing the standard deviation of the sample.

    • 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.

    • 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.

    • 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.

    • 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.

    • 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.

    • getLowerCIVariance

      public double getLowerCIVariance()
      Returns the lower confidence limits for the variance.
      Returns:
      a double containing the lower confidence limits for the variance.

    • getUpperCIVariance

      public double getUpperCIVariance()
      Returns the upper confidence limits for the variance.
      Returns:
      a double the upper confidence limits for the variance.

    • 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 \( \omega^2 = \omega_0^2\) where \(\omega_0^2\) is the null hypothesis value as described in setChiSquaredTestNull.
      Returns:
      an int the degrees of freedom for the chi-squared test.

    • 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 \(\omega^2 = \omega_0^2\) where \(\omega_0^2\) is the null hypothesis value as described in setChiSquaredTestNull.
      Returns:
      a double containing the test statistic 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 \(\omega^2 = \omega_0^2\) where \(\omega_0^2\) 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.

    • 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.