com.imsl.stat

Class SignTest

java.lang.Object

com.imsl.stat.SignTest

All Implemented Interfaces:

Serializable, Cloneable

public class SignTest
extends Object
implements Serializable, Cloneable

Performs a sign test.

Class SignTest tests hypotheses about the proportion p of a population that lies below a value q, where p corresponds to percentage and q corresponds to percentile in the setPercentage and setPercentile methods, respectively. In continuous distributions, this can be a test that q is the 100 p-th percentile of the population from which x was obtained. To carry out testing, SignTest tallies the number of values above q in the number of positive differences \(x[j-1]- {\rm percentile}\) for \(j=1, 2, \ldots, {\rm x.length}\). The binomial probability of the number of values above q in the number of positive differences \(x[j-1]- {\rm percentile}\) for \(j=1,2,\ldots,\ldots, {\rm x.length}\) or more values above q is then computed using the proportion p and the sample size in x (adjusted for the missing observations and ties).

Hypothesis testing is performed as follows for the usual null and alternative hypotheses:

• \(H_0: Pr(x \leq q) \geq p\) (the p-th quantile is at least q)
  \(H_1: Pr(x \leq q) \lt p\)
  Reject \(H_0\) if probability is less than or equal to the significance level
• \(H_0: Pr(x \leq q) \leq p\) (the p-th quantile is at least q)
  \(H_1: Pr(x \leq q) \gt p\)
  Reject \(H_0\) if probability is greater than or equal to 1 minus the significance level
• \(H_0: Pr (x = q) = p\) (the p-th quantile is q)
  \(H_1: Pr((x \leq q) \lt p)\) or \(Pr((x \le q) \gt p)\)
  Reject \(H_0\) if probability is less than or equal to half the significance level or greater than or equal to 1 minus half the significance level

The assumptions are as follows:

1. They are independent and identically distributed.
2. Measurement scale is at least ordinal; i.e., an ordering less than, greater than, and equal to exists in the observations.

Many uses for the sign test are possible with various values of p and q. For example, to perform a matched sample test that the difference of the medians of y and z is 0.0, let p = 0.5, q = 0.0, and \(x_i = y_i - z_i\) in matched observations y and z. To test that the median difference is c, let q = c.

See Also:

Example 1, Example 2, Serialized Form

Constructor Summary

Constructors

Constructor and Description
SignTest(double[] x) Constructor for SignTest.

Method Summary

Modifier and Type	Method and Description
double	compute() Performs a sign test.
int	getNumPositiveDev() Returns the number of positive differences.
int	getNumZeroDev() Returns the number of zero differences.
void	setPercentage(double percentage) Sets the percentage percentile of the population.
void	setPercentile(double percentile) Sets the hypothesized percentile of the population.

Methods inherited from class java.lang.Object

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

Constructor Detail

SignTest

public SignTest(double[] x)

Constructor for SignTest.

Parameters:

x - A double array containing the data.

Method Detail

compute

public final double compute()

Performs a sign test.

Returns:

A double scalar containing the Binomial probability of getNumPositiveDev or more positive differences in x.length - number of zero differences trials. Call this value probability. If using default values, the null hypothesis is that the median equals 0.0.

getNumPositiveDev

public int getNumPositiveDev()

Returns the number of positive differences. Note that the compute method must be invoked first before invoking this method. Otherwise, the return value is 0.

Returns:

An int scalar containing the number of positive differences x[j-1]-percentile for j = 1, 2, ..., x.length.

getNumZeroDev

public int getNumZeroDev()

Returns the number of zero differences. Note that the compute method must be invoked first before invoking this method. Otherwise, the return value is 0.

Returns:

An int scalar containing the number of zero differences (ties) x[j-1]-percentile for j = 1, 2, ..., x.length.

setPercentile

public void setPercentile(double percentile)

Sets the hypothesized percentile of the population.

Parameters:

percentile - A double scalar containing the hypothesized percentile of the population from which x was drawn. Default: percentile = 0.0

setPercentage

public void setPercentage(double percentage)

Sets the percentage percentile of the population.

Parameters:

percentage - A double scalar containing the value in the range (0, 1). percentile is the 100 * percentage percentile of the population. Default: percentage = 0.5.