SignTest Class |
Namespace: Imsl.Stat
The SignTest type exposes the following members.
Name | Description | |
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Compute |
Performs a sign test.
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Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetType | Gets the Type of the current instance. (Inherited from Object.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
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NumPositiveDev |
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.
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NumZeroDev |
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.
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Percentage |
The percentage percentile of the population.
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Percentile |
The hypothesized percentile of the population.
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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 for . The binomial probability of the number of values above q in the number of positive differences for 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:
(the p-th quantile is at least q)
Reject if probability is less than or equal to the significance level.
(the p-th quantile is at least q)
Reject if probability is greater than or equal to 1 minus the significance level.
(the p-th quantile is q)
or
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:
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.