extras (version 0.10.0)

probability_direction: Probability of Direction

Description

The probability of direction (PD) is the proportion of the (posterior) distribution above (right) or below (left) a threshold.

Usage

probability_direction(x, side = "median", threshold = 0, 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.

side

A character vector of length 1 indicating whether to calculate the directional probability for the left tail ("left"; x < threshold), or the right tail ("right"; x > threshold). Defaults to "median", which uses the side of the median of x via direction().

threshold

A number of the threshold value, which is excluded from the interval for the probability.

na_rm

A flag specifying whether to remove missing values.

Details

By default, the direction is based on the side of the median value, but it can be specified to measure support for specific hypotheses. A right-side PD of 0.9 indicates that the interval spanning from the threshold to infinity has a coverage of 90%. Can be used as a measure of certainty in the direction of the estimate (e.g., positive or negative when using a threshold of 0). NOTE: probability estimates of 0 or 1 are corrected towards 0.5 by adding or subtracting 1 / (length(x) + 1), where x is a vector of MCMC samples. Ideally, x should be large enough as to make the correction negligible.

References

Makowski, D., Ben-Shachar, M.S., Chen, S.H.A., and Lüdecke, D. 2019. Indices of Effect Existence and Significance in the Bayesian Framework. Front. Psychol. 10: 2767. tools:::Rd_expr_doi("10.3389/fpsyg.2019.02767").

See Also

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

Examples

x <- rnorm(1e6, qnorm(0.05, lower.tail = TRUE))
probability_direction(x, side = "left")
probability_direction(x, side = "right") # = 1 - probability_direction(x, side = "left")
probability_direction(c(0, 0, 1), side = "right") # returns P(X >0) = 1/3 instead of P(X >= 0) = 1
probability_direction(c(1, 1), side = "right") # p = 1 - 1/(n+1)