extras (version 0.10.0)

pvalue: Bayesian P-Value

Description

A Bayesian p-value (p) is here defined in terms of the quantile-based (1-p) * 100% credible interval (CRI) that just includes a threshold (Kery and Schaub 2011).

Usage

pvalue(x, ..., side = "both", threshold = 0, skeptical = TRUE, na_rm = FALSE)

Value

A number between 0 and 1. If x has NA values but na_rm is FALSE, returns NA_real.

Arguments

x

A numeric vector of MCMC values.

...

Unused.

side

A character vector of length 1 indicating whether to calculate p-values for the left tail ("left"), right tail ("right"), or two-sided ("both"; default).

threshold

A number of the threshold value.

skeptical

A flag specifying whether or not to add one sample to the empty side of the threshold when 100% of samples are on one side. Avoids zero p-values and infinite s-values, and also imposes stronger bounds on directional information than [-n, n], which assume the MCMC samples are independent and representative.

na_rm

A flag specifying whether to remove missing values.

Details

A p-value of 0.05 indicates that the 95% CRI just includes the threshold value.

Note that the function contains the sample-size correction \(p_{c} = p * n / (n + 1)\) to avoid p-values of 0. The function can still return p-values of 1.

When skeptical = TRUE (default), a floor of \(1 / (n + 1)\) is applied to avoid p-values of 0 when all samples are on one side of the threshold. When skeptical = FALSE, p-values of 0 are allowed.

To use as a measure of certainty in the direction of the estimate (i.e., positive or negative), see probability_direction().

For p-values converted to bits, see svalue().

To convert MCMC objects to information, see directional_information().

References

Kery, M., and Schaub, M. 2011. Bayesian population analysis using WinBUGS: a hierarchical perspective. Academic Press, Boston. Available from https://www.vogelwarte.ch/en/research/population-biology/book-bpa/.

See Also

Other summary: direction(), directional_information(), kurtosis(), lower(), probability_direction(), pzeros(), skewness(), svalue(), upper(), variance(), xtr_mean(), xtr_median(), xtr_sd(), zeros(), zscore()

Examples

x <- rnorm(1e6, qnorm(0.05, lower.tail = TRUE))
pvalue(x) # should be 0.05 * 2
pvalue(x, side = "left") # should be 0.95
pvalue(x, side = "right") # should be 0.05
pvalue(rep(1, 10)) # skeptical = TRUE (default) avoids p = 0
pvalue(rep(1, 10), skeptical = FALSE) # skeptical = FALSE allows p = 0