sign_test_pv: Sign Tests

In DiscreteTests: Vectorised Computation of P-Values and Their Supports for Several Discrete Statistical Tests

Sign Tests

Description

sign_test_pv() performs an exact or approximate sign test about the median of a distribution. It supports both one-sample and two-sample paired tests. In contrast to other implementations, it is vectorised, only calculates p-values, and offers a normal approximation of their computation. Furthermore, it is capable of returning the discrete p-value supports, i.e. all observable p-values under a null hypothesis. Multiple tests can be evaluated simultaneously. In two-sided tests, several procedures of obtaining the respective p-values are implemented.

Usage

sign_test_pv(
  x,
  y = NULL,
  mu = 0,
  alternative = "two.sided",
  exact = TRUE,
  correct = TRUE,
  simple_output = FALSE
)

Arguments

x	numerical vector forming the sample to be tested or a list of numerical vectors for multiple tests.
y	numerical vector forming the second sample to be tested or a list of numerical vectors for multiple tests; if y = NULL (the default), the one-sample version is performed; for two-sample tests, all sample pairs must have the same length.
mu	numerical vector of hypothesised median(s) for one-sample tests or median(s) of differences for two-sample tests.
alternative	character vector that indicates the alternative hypotheses; each value must be one of "two.sided" (the default), "less" or "greater".
exact	single logical value that indicates whether p-values are to be calculated by exact computation (TRUE; the default) or by a continuous approximation (FALSE).
correct	single logical value that indicates if a continuity correction in the normal approximation is to be applied (TRUE; the default) or not (FALSE). Ignored, if exact = TRUE.
simple_output	logical value that indicates whether an R6 class object, including the tests' parameters and support sets, i.e. all observable p-values under each null hypothesis, is to be returned (see below).

Details

For the one-sample case, the sign test counts the number of observations in x that exceed the hypothesised median mu. Observations exactly equal to mu (ties) are discarded. Under the null hypothesis, the number of positive signs follows a Binomial(n, 0.5) distribution, where n is the number of non-tied observations.

For the two-sample paired case (when y is supplied), the pairwise differences d_i = x_i - y_i - \mu are computed first. The sign test is then applied to these differences.

If x is a list, multiple tests are evaluated simultaneously. The parameters x, y (if supplied and a list), mu, and alternative are vectorised. They are replicated automatically to have the same lengths. This allows multiple hypotheses to be tested simultaneously.

The sign test is a special case of the binomial test. In contrast to binom_test_pv(), sign_test_pv() does not allow specifying exact two-sided p-value calculation procedures. The reason is that the exact sign test always tests for a probability of 0.5, in which case all these exact two-sided p-value computation methods yield exactly the same results.

Value

If simple.output = TRUE, a vector of computed p-values is returned. Otherwise, the output is a DiscreteTestResults R6 class object, which also includes the p-value supports and testing parameters. These have to be accessed by public methods, e.g. ⁠$get_pvalues()⁠.

References

Dixon, W. J. and Mood, A. M. (1946). The statistical sign test. Journal of the American Statistical Association, 41(236), pp. 557–566. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.1946.10501898")}

See Also

binom_test_pv(), stats::binom.test()

Examples

# One-sample sign test: test whether median equals 3
x <- c(1, 5, 2, 7, 6, 8, 4)
results_1s <- sign_test_pv(x, mu = 3)
print(results_1s)
results_1s$get_pvalues()
results_1s$get_pvalue_supports()

# Paired two-sample sign test: test whether difference of medians equals 1
x2 <- c(6, 8, 2, 4, 5)
y2 <- c(3, 5, 4, 2, 6)
results_2s <- sign_test_pv(x2, y2, mu = 1)
print(results_2s)
results_2s$get_pvalues()

# Multiple tests simultaneously, one-sided p-values (one-sample, list input)
xs <- list(c(1, 5, 2, 7, 6, 8, 4), c(2, 4, 6, 1, 9))
results_l <- sign_test_pv(xs, mu = c(3, 5), alternative = "greater")
print(results_l)
results_l$get_pvalues()

# Normal-approximated (one-sample, list input)
results_a <- sign_test_pv(xs, mu = c(3, 5), exact = FALSE)
print(results_a)
results_a$get_pvalues()

DiscreteTests documentation built on Sept. 2, 2026, 9:06 a.m.