SignTest Class

Performs a sign test.

For a list of all members of this type, see SignTest Members.

System.Object
Imsl.Stat.SignTest

public class SignTest

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

Remarks

Class SignTest tests hypotheses about the proportion p of a population that lies below a value q, where p and q corresponds to the Percentage and Percentile properties, 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 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 if probability is greater than or equal to 1 minus the significance level.
(the p-th quantile is q)

$H_1: Pr((x \leq q) \lt p)$ or $Pr((x \le q) \gt p)$

Reject 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:

They are independent and identically distributed.
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 in matched observations y and z. To test that the median difference is c, let q = c.

Requirements

Namespace: Imsl.Stat

Assembly: ImslCS (in ImslCS.dll)

SignTest Class

Thread Safety

Remarks

Requirements

See Also