Convert p-values to (pseudo) Bayes Factors. This transformation has been
suggested by Wagenmakers (2022), but is based on a vast amount of assumptions.
It might therefore be not reliable. Use at your own risks. For more accurate
approximate Bayes factors, use `bic_to_bf()`

instead.

## Usage

```
p_to_bf(x, ...)
# S3 method for class 'numeric'
p_to_bf(x, log = FALSE, n_obs = NULL, ...)
# Default S3 method
p_to_bf(x, log = FALSE, ...)
```

## Arguments

- x
A (frequentist) model object, or a (numeric) vector of p-values.

- ...
Other arguments to be passed (not used for now).

- log
Wether to return log Bayes Factors.

**Note:**The`print()`

method always shows`BF`

- the`"log_BF"`

column is only accessible from the returned data frame.- n_obs
Number of observations. Either length 1, or same length as

`p`

.

## References

Wagenmakers, E.J. (2022). Approximate objective Bayes factors from p-values and sample size: The 3p(sqrt(n)) rule. Preprint available on ArXiv: https://psyarxiv.com/egydq

## See also

`bic_to_bf()`

for more accurate approximate Bayes factors.

## Examples

```
data(iris)
model <- lm(Petal.Length ~ Sepal.Length + Species, data = iris)
p_to_bf(model)
#> Pseudo-BF (against NULL)
#>
#> Parameter | p | BF
#> -------------------------------------
#> (Intercept) | < .001 | 2.71e+09
#> Sepal.Length | < .001 | 2.43e+26
#> Speciesversicolor | < .001 | 2.82e+64
#> Speciesvirginica | < .001 | 5.53e+68
# Examples that demonstrate comparison between
# BIC-approximated and pseudo BF
# --------------------------------------------
m0 <- lm(mpg ~ 1, mtcars)
m1 <- lm(mpg ~ am, mtcars)
m2 <- lm(mpg ~ factor(cyl), mtcars)
# In this first example, BIC-approximated BF and
# pseudo-BF based on p-values are close...
# BIC-approximated BF, m1 against null model
bic_to_bf(BIC(m1), denominator = BIC(m0))
#> [1] 222.005
# pseudo-BF based on p-values - dropping intercept
p_to_bf(m1)[-1, ]
#> Pseudo-BF (against NULL)
#>
#> Parameter | p | BF
#> ---------------------------
#> am | < .001 | 206.74
# The second example shows that results from pseudo-BF are less accurate
# and should be handled wit caution!
bic_to_bf(BIC(m2), denominator = BIC(m0))
#> [1] 45355714
p_to_bf(anova(m2), n_obs = nrow(mtcars))
#> Pseudo-BF (against NULL)
#>
#> Parameter | p | BF
#> -------------------------------
#> factor(cyl) | < .001 | 1.18e+07
```