When it comes to drawing statistical conclusions from data, classical (frequentist) inferential procedures are of widespread use. Yet, their results are subject to constant misuse (García-Pérez, 2012) and misinterpretation (Hoekstra et. al., 2014), thus impairing the validity of statistical and scientific conclusions. Recent criticism against the Null Hypothesis Testing Procedure (NHSTP) has propelled the development and refinement of Bayesian hypothesis testing procedures, which are deemed free of the problems that hamper frequentist analyses.

The present app performs two-sided tests for Pearson's correlation in a Bayesian
hypothesis testing framework. The Bayes Factor (BF), upon which statistical conclusions
are based, quantifies the evidence in favor of a given hypothesis, as opposed to another
(Kass & Raftery, 1995). Here, a null hypothesis *H _{0}: ρ = 0* is
tested against an alternative hypothesis

The app consists on four different tabs that are organized as follows. All tabs perform the above test, showing its corresponding prior and posterior distributions, as well as the value of the BF for the null hypothesis (BF01) and the value of the BF for the alternative (BF10). In addition, the app displays the scatterplot and histograms of both variables, as well as a summary of some inferential statistics.

The **first tab** simulates data from a bivariate
Normal distribution as shown by Demritas (2004). The user can change
the value of the true linear correlation, the sample size, and the width of
the stretched Beta prior distribution. The **second tab **incorporates a more
versatile interface for generating data, where the user can add individual
observations by clicking anywhere on the scatterplot. And whilst the **third
tab **includes different sample data sets, the **fourth** and final **tab** allows the
user to upload their own data sets.

All in all, the "Bayesian correlation analysis" app shows how the results of Bayesian procedures vary in the light of changes regarding data and prior beliefs.

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*ArXiv preprint arXiv:1510.01188.* - Wagenmakers, E.-J., Verhagen, A. J., & Ly, A. (2016). How to quantify the evidence for the absence of a correlation.
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TquanT is co-funded by
the Erasmus+ Programme of the European Commission.

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© 2016, Berenice López-Casal, Universidad Complutense de Madrid, Spain & E.J. Wagenmakers, University of Amsterdam, The Netherlands