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Author: DominiqueMakowski

docs/_posts/2018-06-11-bayesian_correlation.md

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+---
+layout: post
+title: "Easy APA Formatted Bayesian Correlation"
+author: Dominique Makowski
+author_web: https://dominiquemakowski.github.io/
+date: 2018-06-11
+summary: Perform, interpret and format Bayesian correlations in one line.
+---
+
+
+
+-   [Traditional Correlation](#traditional-correlation)
+-   [Bayesian APA formatted Correlation](#bayesian-apa-formatted-correlation)
+-   [Indices](#indices)
+-   [Posterior](#posterior)
+-   [Credits](#credits)
+
+
+**The Bayesian framework is the right way to go for psychological science.** To facilitate its use for newcommers, we implemented the `bayes_cor.test` function in the [psycho package](https://github.com/neuropsychology/psycho.R), a **user-friendly wrapper** for the `correlationBF` function of the great [`BayesFactor`](https://richarddmorey.github.io/BayesFactor/) package by Richard D. Morey.
+
+Traditional Correlation
+=======================
+
+Let's first perform a traditional correlation.
+
+``` r
+# devtools::install_github("neuropsychology/psycho.R")  # Install the latest psycho version
+
+# Load packages
+library(tidyverse)
+library(psycho)
+
+# Import data
+df <- psycho::affective
+
+cor.test(df$Concealing, df$Tolerating)
+```
+
+
+        Pearson's product-moment correlation
+
+    data:  df$Concealing and df$Tolerating
+    t = 2.611, df = 1249, p-value = 0.009136
+    alternative hypothesis: true correlation is not equal to 0
+    95 percent confidence interval:
+     0.01832974 0.12857724
+    sample estimates:
+           cor 
+    0.07367859 
+
+There is a **significant** (*whatever that means*), yet **weak positive** correlation between Concealing and Tolerating affective styles.
+
+Bayesian APA formatted Correlation
+==================================
+
+And now, see how quickly we can do a Bayesian correlation:
+
+``` r
+bayes_cor.test(df$Concealing, df$Tolerating)
+```
+
+    Results of the Bayesian correlation indicate anecdotal evidence (BF = 1.95) in favour of a positive association between df$Concealing and df$Tolerating (r = 0.073, MAD = 0.028, 90% CI [0.023, 0.12]). The correlation can be considered as small or very small with respective probabilities of 16.55% and 83.06%.
+
+The results are roughly the same, but neatly dissociate the likelihood in favour or against the null hypothesis (using the [Bayes Factor](https://www.r-bloggers.com/what-does-a-bayes-factor-feel-like/)), from the "significance" (wether a portion of the *Credible Interval* covers 0), from the effect size (interpreted here with [Cohen's (1988) rules of thumb](https://github.com/neuropsychology/psycho.R/blob/master/R/interpret_r.R#L142)). Critically, **you can, now, simply copy/paste this output to your manuscript!** It includes and formats the Bayes Factor, the median (a good point-estimate, close to the *r* estimated in frequentist correlation), MAD (robust equivalent of SD for median) and *credible* interval (CI) of the posterior distribution, as well as effect size interpretation.
+
+Indices
+=======
+
+We can have access to more indices with the `summary`:
+
+``` r
+results <- bayes_cor.test(df$Concealing, df$Tolerating)
+summary(results)
+```
+
+|                                                   |  Median|   MAD|  Mean|    SD|  CI\_lower|  CI\_higher|    MPE|    BF|  Overlap| Rope      |
+|---------------------------------------------------|-------:|-----:|-----:|-----:|----------:|-----------:|------:|-----:|--------:|:----------|
+| df\$Concealing/df\$Tolerating |    0.07|  0.03|  0.07|  0.03|       0.03|        0.12|  99.56|  1.95|    19.43| Undecided |
+
+Those indices include the ROPE decision criterion (see [Kruschke, 2018](http://journals.sagepub.com/doi/abs/10.1177/2515245918771304)) as well as the Maximum Probability of Effect (MPE, the probability that an effect is negative or positive and different from 0).
+
+Posterior
+=========
+
+We can easily extract the posterior distribution to visualize the probability of possible effects.
+
+``` r
+posterior <- results$values$posterior
+
+plot(density(posterior))
+```
+
+<img src="https://raw.githubusercontent.com/neuropsychology/psycho.R/master/docs/_posts/2018-06-11-bayesian_correlation_files/figure-markdown_github/unnamed-chunk-6-1.png" style="display: block; margin: auto;" />
+
+Credits
+=======
+
+This package helped you? Don't forget to cite the various packages you used :)
+
+You can cite `psycho` as follows:
+
+-   Makowski, (2018). *The psycho Package: an Efficient and Publishing-Oriented Workflow for Psychological Science*. Journal of Open Source Software, 3(22), 470. <https://doi.org/10.21105/joss.00470>

docs/_posts/2018-06-11-bayesian_correlation_files/figure-markdown_github/unnamed-chunk-6-1.png

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+---
+title: "Easy APA Formatted Bayesian Correlation"
+layout: post
+output:
+  html_document:
+    df_print: paged
+    toc: yes
+  md_document:
+    toc: yes
+    variant: markdown_github
+author: "Dominique Makowski"
+date: "`r Sys.Date()`"
+editor_options: 
+  chunk_output_type: console
+---
+
+
+```{r message=FALSE, warning=FALSE, include=FALSE}
+library(knitr)
+```
+
+**The Bayesian framework is the right way to go for psychological science.** To facilitate its use for newcommers, we implemented the `bayes_cor.test` function in the [psycho package](https://github.com/neuropsychology/psycho.R), a **user-friendly wrapper** for the `correlationBF` function of the great [`BayesFactor`](https://richarddmorey.github.io/BayesFactor/) package by Richard D. Morey.
+
+# Traditional Correlation
+
+Let's first perform a traditional correlation.
+
+```{r, fig.width=7, fig.height=4.5, eval = TRUE, results='markup', fig.align='center', comment=NA, message=FALSE, warning=FALSE}
+# devtools::install_github("neuropsychology/psycho.R")  # Install the latest psycho version
+
+# Load packages
+library(tidyverse)
+library(psycho)
+
+# Import data
+df <- psycho::affective
+
+cor.test(df$Concealing, df$Tolerating)
+```
+
+There is a **significant** (*whatever that means*), yet **weak positive** correlation between Concealing and Tolerating affective styles.
+
+
+# Bayesian APA formatted Correlation
+
+And now, see how quickly we can do a Bayesian correlation: 
+
+```{r, fig.width=7, fig.height=4.5, eval = TRUE, results='markup', fig.align='center', comment=NA, message=FALSE, warning=FALSE}
+bayes_cor.test(df$Concealing, df$Tolerating)
+```
+
+The results are roughly the same, but neatly dissociate the likelihood in favour or against the null hypothesis (using the [Bayes Factor](https://www.r-bloggers.com/what-does-a-bayes-factor-feel-like/)), from the "significance" (wether a portion of the *Credible Interval* covers 0), from the effect size (interpreted here with [Cohen's (1988) rules of thumb](https://github.com/neuropsychology/psycho.R/blob/master/R/interpret_r.R#L142)). Critically, **you can, now, simply copy/paste this output to your manuscript!** It includes and formats the Bayes Factor, the median (a good point-estimate, close to the *r* estimated in frequentist correlation), MAD (robust equivalent of SD for median) and *credible* interval (CI) of the posterior distribution, as well as effect size interpretation.
+
+# Indices
+
+We can have access to more indices with the `summary`:
+
+```{r, fig.width=7, fig.height=4.5, eval = TRUE, results='hide', fig.align='center', comment=NA, message=FALSE, warning=FALSE}
+results <- bayes_cor.test(df$Concealing, df$Tolerating)
+summary(results)
+```
+```{r, fig.width=7, fig.height=4.5, echo=FALSE, eval = TRUE, fig.align='center', comment=NA, message=FALSE, warning=FALSE}
+knitr::kable(summary(results), digits=2)
+```
+
+Those indices include the ROPE decision criterion (see [Kruschke, 2018](http://journals.sagepub.com/doi/abs/10.1177/2515245918771304)) as well as the Maximum Probability of Effect (MPE, the probability that an effect is negative or positive and different from 0).
+
+# Posterior 
+
+We can easily extract the posterior distribution to visualize the probability of possible effects.
+
+```{r, fig.width=7, fig.height=4.5, eval = TRUE, fig.align='center', comment=NA, message=FALSE, warning=FALSE}
+posterior <- results$values$posterior
+
+plot(density(posterior))
+```
+
+
+
+# Credits
+
+This package helped you? Don't forget to cite the various packages you used :)
+
+You can cite `psycho` as follows:
+
+- Makowski, (2018). *The psycho Package: an Efficient and Publishing-Oriented Workflow for Psychological Science*. Journal of Open Source Software, 3(22), 470. https://doi.org/10.21105/joss.00470