# Reporting Guidelines

These guidelines can be referred to by citing the package:

# Reporting Guidelines

Based on the previous **comparison of point-estimates** and **indices of effect existence**, we can draw the following recommendations.

To minimally **describe the posterior distribution** of a parameter, we suggest reporting 1) the **median** as an index of centrality, 2) the **89% CI** (using HDI rather than quantiles) as an index of centrality and, in the context of null-hypothesis testing, the **Probability of Direction (***pd*) for effect existence and, especially in the context of confirmatory analyses, the **ROPE percentage** (full, *i.e.*, based on the full posterior distribution) with an explicitly specified range for effect significance.

# Effect *Existence* and *significance*

The **pd** and the **ROPË** are two indices that give different and independent information: The **pd** is a marker of **existence**, consistency and direction of a parameter (whether a parameter has a consistent effect in one or another direction), whereas the percentage in **ROPE** is a index of **significance** (in its primary meaning); informing us whether a parameter is related or not to a non-negligible change (in terms of magnitude) in the outcome.

## Interpretation Rules of Thumb

**The following thresholds are presented as landmarks only, and any use of such “labels” should be explicitly justified. Please consider with caution.**

**Probability of Direction (***p*d): In most cases, it seems that the *pd* corresponds to the frequentist one-sided *p* value through the formula `p value = (1-pd/100)`

and to the two-sided *p* value (the most commonly reported) through the formula `p value = 2*(1-pd/100)`

. Thus, a `pd`

of `95%`

, `97.5%`

`99.5%`

and `99.95%`

corresponds approximately to a two-sided *p* value of respectively `.1`

, `.05`

, `.01`

and `.001`

. Thus, for convience, we recommend using the following reference values:

*pd* **<= 95%** ~ *p* > .1: uncertain
*pd* **> 95%** ~ *p* < .1: possibly existing
*pd* **> 97%**: likely existing
*pd* **> 99%**: probably existing
*pd* **> 99.9%**: certainly existing

**ROPE (full)**: Extra caution is required as its interpretation highly depends on other parameters such as sample size and ROPE range.

**> 99%** in ROPE: negligible (we can accept the null hypothesis)
**> 97.5%** in ROPE: probably negligible
**<= 97.5%** & **>= 2.5%** in ROPE: undecided significance
**< 2.5%** in ROPE: probably significant
**< 1%** in ROPE: significant (we can reject the null hypothesis)

*Note: If you have any advice, opinion or such, we encourage you to let us know by opening an discussion thread or making a pull request.*

## Template Sentence

Based on these suggestions, a template sentence for minimal reporting of a parameter based on its posterior distribution could be:

- “the effect of
*X* has a probability of **pd** of being *negative* (Median = **median**, 89% CI [***…***, ***…***]) and can be considered as *significant* (**ROPE**% in ROPE).”