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:

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 in matched observations y and z. To test that the median difference is c, let q = c.