---
title: "Reporting Guidelines"
output: 
  rmarkdown::html_vignette:
    toc: true
    fig_width: 10.08
    fig_height: 6
tags: [r, bayesian, posterior, test]
vignette: >
  %\VignetteIndexEntry{Reporting Guidelines}
  \usepackage[utf8]{inputenc}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  chunk_output_type: console
bibliography: bibliography.bib
csl: apa.csl
---

```{r message=FALSE, warning=FALSE, include=FALSE}
library(knitr)
options(knitr.kable.NA = '')
knitr::opts_chunk$set(comment=">")
options(digits=2)
```


This vignette can be referred to by citing the package:

- Makowski, D., Ben-Shachar, M. S., \& Lüdecke, D. (2019). *bayestestR: Describing Effects and their Uncertainty, Existence and Significance within the Bayesian Framework*. Journal of Open Source Software, 4(40), 1541. https://doi.org/10.21105/joss.01541
- Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., \& Lüdecke, D. (2019). *Indices of Effect Existence and Significance in the Bayesian Framework*. Frontiers in Psychology 2019;10:2767. [10.3389/fpsyg.2019.02767](https://doi.org/10.3389/fpsyg.2019.02767)

---

# Reporting Guidelines

## How to describe and report the parameters of a model

A Bayesian analysis returns a posterior distribution for each parameter (or
*effect*). To minimally describe these distributions, we recommend reporting a
point-estimate of [centrality](https://en.wikipedia.org/wiki/Central_tendency)
as well as information characterizing the estimation uncertainty (the
[dispersion](https://en.wikipedia.org/wiki/Statistical_dispersion)).
Additionally, one can also report indices of effect existence and/or
significance.

Based on the previous [**comparison of point-estimates**](https://easystats.github.io/bayestestR/articles/indicesEstimationComparison.html)
and [**indices of effect existence**](https://www.frontiersin.org/articles/10.3389/fpsyg.2019.02767/full),
we can draw the following recommendations.

### **Centrality**

We suggest reporting the
[**median**](https://easystats.github.io/bayestestR/reference/point_estimate.html)
as an index of centrality, as it is more robust compared to the
[mean](https://easystats.github.io/bayestestR/reference/point_estimate.html) or
the [MAP
estimate](https://easystats.github.io/bayestestR/reference/map_estimate.html).
However, in case of a severely skewed posterior distribution, the MAP estimate
could be a good alternative.
 

### **Uncertainty** 

The [**95\% or 89\% Credible Intervals (CI)**](https://easystats.github.io/bayestestR/articles/credible_interval.html)
are two reasonable ranges to characterize the uncertainty related to the
estimation (see [here](https://easystats.github.io/bayestestR/articles/credible_interval.html) for a discussion about the differences between these two values). We also recommend computing the CIs based on the [HDI](https://easystats.github.io/bayestestR/reference/hdi.html) rather than [quantiles](https://easystats.github.io/bayestestR/reference/ci.html), favouring
probable over central values.

Note that a CI based on the quantile (equal-tailed interval) might be more
appropriate in case of transformations (for instance when transforming log-odds
to probabilities). Otherwise, intervals that originally do not cover the null
might cover it after transformation (see
[here](https://easystats.github.io/bayestestR/articles/credible_interval.html#different-types-of-cis)).


### **Existence** 

```{r echo=FALSE, fig.cap="Reviewer 2 (circa a long time ago in a galaxy far away).", fig.align='center', out.width="60%"}
knitr::include_graphics("https://github.com/easystats/easystats/raw/master/man/figures/bayestestR/watto.jpg")
```

The Bayesian framework can neatly delineate and quantify different aspects of
hypothesis testing, such as effect *existence* and *significance*. The most
straightforward index to describe existence of an effect is the [**Probability of Direction (pd)**](https://easystats.github.io/bayestestR/articles/probability_of_direction.html),
representing the certainty associated with the most probable direction (positive
or negative) of the effect. This index is easy to understand, simple to
interpret, straightforward to compute, robust to model characteristics, and
independent from the scale of the data.

Moreover, it is strongly correlated with the frequentist **p*-value**, and can
thus be used to draw parallels and give some reference to readers non-familiar
with Bayesian statistics. A **two-sided *p*-value** of respectively `.1`, `.05`,
`.01` and `.001` correspond approximately to a ***pd*** of 95\%, 97.5\%,
99.5\% and 99.95\%. 

Thus, for convenience, we suggest the following reference values as an
interpretation helpers:

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

### **Significance** 

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. We suggest
reporting the **percentage of the full posterior distribution** (the *full*
ROPE) instead of a given proportion of CI in the ROPE, which appears to be more
sensitive (especially to delineate highly significant effects). Rather than
using it as a binary, all-or-nothing decision criterion, such as suggested by
the original [equivalence test](https://easystats.github.io/bayestestR/articles/region_of_practical_equivalence.html#equivalence-test),
we recommend using the percentage as a *continuous* index of significance.
However, based on [simulation data](https://www.frontiersin.org/articles/10.3389/fpsyg.2019.02767/full), we
suggest the following reference values as an interpretation helpers:


  - **\> 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 that extra caution is required as its interpretation highly depends on other parameters such as sample size and ROPE range (see [here](https://easystats.github.io/bayestestR/articles/region_of_practical_equivalence.html#sensitivity-to-parameters-scale))*.


### **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 [ ***HDI<sub>low</sub>*** , ***HDI<sub>high</sub>*** ] and
can be considered as *significant* (***ROPE***\% in ROPE)."

## How to compare different models

Although it can also be used to assess effect existence and significance, the
**Bayes factor (BF)** is a versatile index that can be used to directly compare
different models (or data generation processes). The [Bayes factor](https://easystats.github.io/bayestestR/articles/bayes_factors.html) is a
ratio that informs us by how much more (or less) likely the observed data are
under two compared models - usually a model *with* versus a model *without* the
effect. Depending on the specifications of the null model (whether it is a
point-estimate (e.g., **0**) or an interval), the Bayes factor could be used
both in the context of effect existence and significance.

In general, a Bayes factor greater than 1 is taken as evidence in favour of one
of the model (in the nominator), and a Bayes factor smaller than 1 is taken as
evidence in favour of the other model (in the denominator). Several rules of
thumb exist to help the interpretation (see
[here](https://easystats.github.io/effectsize/reference/interpret_bf.html)),
with **\> 3** being one common threshold to categorize non-anecdotal evidence.
 

### **Template Sentence** 

When reporting Bayes factors (BF), one can use the following sentence: 

> "There is *moderate evidence* in favour of an *absence* of effect of *x* (BF = *BF*)."

# Suggestions

If you have any advice, opinion or such, we encourage you to let us know by
opening an [discussion thread](https://github.com/easystats/bayestestR/issues)
or making a pull request.
