# p_significance: Practical Significance (ps) In bayestestR: Understand and Describe Bayesian Models and Posterior Distributions

## Description

Compute the probability of Practical Significance (ps), which can be conceptualized as a unidirectional equivalence test. It returns the probability that effect is above a given threshold corresponding to a negligible effect in the median's direction. Mathematically, it is defined as the proportion of the posterior distribution of the median sign above the threshold.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```p_significance(x, ...) ## S3 method for class 'numeric' p_significance(x, threshold = "default", ...) ## S3 method for class 'emmGrid' p_significance(x, threshold = "default", ...) ## S3 method for class 'stanreg' p_significance( x, threshold = "default", effects = c("fixed", "random", "all"), component = c("location", "all", "conditional", "smooth_terms", "sigma", "distributional", "auxiliary"), parameters = NULL, verbose = TRUE, ... ) ## S3 method for class 'brmsfit' p_significance( x, threshold = "default", effects = c("fixed", "random", "all"), component = c("conditional", "zi", "zero_inflated", "all"), parameters = NULL, verbose = TRUE, ... ) ```

## Arguments

 `x` Vector representing a posterior distribution. Can also be a `stanreg` or `brmsfit` model. `...` Currently not used. `threshold` The threshold value that separates significant from negligible effect. If `"default"`, the range is set to `0.1` if input is a vector, and based on `rope_range()` if a Bayesian model is provided. `effects` Should results for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated. `component` Should results for all parameters, parameters for the conditional model or the zero-inflated part of the model be returned? May be abbreviated. Only applies to brms-models. `parameters` Regular expression pattern that describes the parameters that should be returned. Meta-parameters (like `lp__` or `prior_`) are filtered by default, so only parameters that typically appear in the `summary()` are returned. Use `parameters` to select specific parameters for the output. `verbose` Toggle off warnings.

## Details

`p_significance()` returns the proportion of a probability distribution (`x`) that is outside a certain range (the negligible effect, or ROPE, see argument `threshold`). If there are values of the distribution both below and above the ROPE, `p_significance()` returns the higher probability of a value being outside the ROPE. Typically, this value should be larger than 0.5 to indicate practical significance. However, if the range of the negligible effect is rather large compared to the range of the probability distribution `x`, `p_significance()` will be less than 0.5, which indicates no clear practical significance.

## Value

Values between 0 and 1 corresponding to the probability of practical significance (ps).

## Note

There is also a `plot()`-method implemented in the see-package.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```library(bayestestR) # Simulate a posterior distribution of mean 1 and SD 1 # ---------------------------------------------------- posterior <- rnorm(1000, mean = 1, sd = 1) p_significance(posterior) # Simulate a dataframe of posterior distributions # ----------------------------------------------- df <- data.frame(replicate(4, rnorm(100))) p_significance(df) ## Not run: # rstanarm models # ----------------------------------------------- if (require("rstanarm")) { model <- rstanarm::stan_glm(mpg ~ wt + cyl, data = mtcars, chains = 2, refresh = 0 ) p_significance(model) } ## End(Not run) ```

bayestestR documentation built on May 31, 2021, 9:06 a.m.