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

```
p_significance(x, ...)
# S3 method for class 'numeric'
p_significance(x, threshold = "default", ...)
# S3 method for class 'get_predicted'
p_significance(
x,
threshold = "default",
use_iterations = FALSE,
verbose = TRUE,
...
)
# S3 method for class 'data.frame'
p_significance(x, threshold = "default", rvar_col = NULL, ...)
# 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, which can have following possible values:

`"default"`

, in which case the range is set to`0.1`

if input is a vector, and based on`rope_range()`

if a (Bayesian) model is provided.a single numeric value (e.g., 0.1), which is used as range around zero (i.e. the threshold range is set to -0.1 and 0.1, i.e. reflects a symmetric interval)

a numeric vector of length two (e.g.,

`c(-0.2, 0.1)`

), useful for asymmetric intervals.

- use_iterations
Logical, if

`TRUE`

and`x`

is a`get_predicted`

object, (returned by`insight::get_predicted()`

), the function is applied to the iterations instead of the predictions. This only applies to models that return iterations for predicted values (e.g.,`brmsfit`

models).- verbose
Toggle off warnings.

- rvar_col
A single character - the name of an

`rvar`

column in the data frame to be processed. See example in`p_direction()`

.- 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.

## 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.

## Note

There is also a `plot()`

-method implemented in the see-package.

## Examples

```
library(bayestestR)
# Simulate a posterior distribution of mean 1 and SD 1
# ----------------------------------------------------
posterior <- rnorm(1000, mean = 1, sd = 1)
p_significance(posterior)
#> Practical Significance (threshold: 0.10)
#>
#> Parameter | ps
#> ----------------
#> Posterior | 0.80
# Simulate a dataframe of posterior distributions
# -----------------------------------------------
df <- data.frame(replicate(4, rnorm(100)))
p_significance(df)
#> Practical Significance (threshold: 0.10)
#>
#> Parameter | ps
#> ----------------
#> X1 | 0.51
#> X2 | 0.55
#> X3 | 0.47
#> X4 | 0.47
# \donttest{
# rstanarm models
# -----------------------------------------------
model <- rstanarm::stan_glm(mpg ~ wt + cyl,
data = mtcars,
chains = 2, refresh = 0
)
p_significance(model)
#> Practical Significance (threshold: 0.60)
#>
#> Parameter | ps
#> ------------------
#> (Intercept) | 1.00
#> wt | 1.00
#> cyl | 0.98
# }
```