Package 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:

  • Constructor Details

    • SignTest

      public SignTest(double[] x)
      Constructor for SignTest.
      Parameters:
      x - A double array containing the data.

  • Method Details

    • 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.