poisson_test_pv {DiscreteTests}

Poisson Test

Description

poisson_test_pv() performs an exact or approximate Poisson test about the rate parameter of a Poisson distribution. In contrast to stats::poisson.test(), 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.

Note: Please use poisson_test_pv()! The older poisson.test.pv() is deprecated in order to migrate to snake case. It will be removed in a future version.

Usage

poisson_test_pv(
  x,
  lambda = 1,
  alternative = "two.sided",
  ts_method = "minlike",
  exact = TRUE,
  correct = TRUE,
  simple_output = FALSE
)

poisson.test.pv(
  x,
  lambda = 1,
  alternative = "two.sided",
  ts.method = "minlike",
  exact = TRUE,
  correct = TRUE,
  simple.output = FALSE
)

Arguments

x

integer vector giving the number of events.

lambda

non-negative numerical vector of hypothesised rate(s).

alternative

character vector that indicates the alternative hypotheses; each value must be one of "two.sided" (the default), "less" or "greater".

ts_method, ts.method

single character string that indicates the two-sided p-value computation method (if any value in alternative equals "two.sided") and must be one of "minlike" (the default), "blaker", "absdist" or "central" (see details). Ignored, if exact = FALSE.

exact

logical value that indicates whether p-values are to be calculated by exact computation (exact = TRUE; the default) or by a continuous approximation.

correct

logical value that indicates if a continuity correction is to be applied (correct = TRUE; the default) or not. Ignored, if exact = TRUE.

simple_output, 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

The parameters x, lambda and alternative are vectorised. They are replicated automatically to have the same lengths. This allows multiple null hypotheses to be tested simultaneously.

Since the Poisson distribution itself has an infinite support, so do the p-values of exact Poisson tests. Thus supports only contain p-values that are not rounded off to 0.

For exact computation, various procedures of determining two-sided p-values are implemented.

"minlike"

The standard approach in stats::fisher.test() and stats::binom.test(). The probabilities of the likelihoods that are equal or less than the observed one are summed up. In Hirji (2006), it is referred to as the Probability-based approach.

"blaker"

The minima of the observations' lower and upper tail probabilities are combined with the opposite tail not greater than these minima. More details can be found in Blaker (2000) or Hirji (2006), where it is referred to as the Combined Tails method.

"absdist"

The probabilities of the absolute distances from the expected value that are greater than or equal to the observed one are summed up. In Hirji (2006), it is referred to as the Distance from Center approach.

"central"

The smaller values of the observations' simply doubles the minimum of lower and upper tail probabilities. In Hirji (2006), it is referred to as the Twice the Smaller Tail method.

For non-exact (i.e. continuous approximation) approaches, ts_method is ignored, since all its methods would yield the same p-values. More specifically, they all converge to the doubling approach as in ts_mthod = "central".

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

Blaker, H. (2000) Confidence curves and improved exact confidence intervals for discrete distributions. Canadian Journal of Statistics, 28(4), pp. 783-798. doi:10.2307/3315916

Hirji, K. F. (2006). Exact analysis of discrete data. New York: Chapman and Hall/CRC. pp. 55-83. doi:10.1201/9781420036190

See Also

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

Examples

# Constructing
k <- c(4, 2, 2, 14, 6, 9, 4, 0, 1)
lambda <- c(3, 2, 1)

# Computation of exact two-sided p-values ("blaker") and their supports
results_ex  <- poisson_test_pv(k, lambda, ts_method = "blaker")
raw_pvalues <- results_ex$get_pvalues()
pCDFlist    <- results_ex$get_pvalue_supports()

# Computation of normal-approximated one-sided p-values ("less") and their supports
results_ap  <- poisson_test_pv(k, lambda, "less", exact = FALSE)
raw_pvalues <- results_ap$get_pvalues()
pCDFlist    <- results_ap$get_pvalue_supports()