Probability of direction
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In Bayesian statistics, the Probability of Direction (pd) is a measure of effect existence representing the certainty with which an effect is positive or negative.[1] This index is numerically similar to the frequentist p-value.[2]
Definition
It is mathematically defined as the proportion of the posterior distribution that is of the median's sign. It typically varies between 50% and 100%.
History
The original formulation of this index and its usage in Bayesian statistics can be found in the psycho software documentation under the appellation Maximum Probability of Effect (MPE).[3][4] Similar formulations have also been described in the context of bootstrapped parameters interpretation.[citation needed]
Properties
The probability of direction is typically independent from the statistical model, as it is solely based on the posterior distribution and does not require any additional information from the data or the model. Contrary to indices related to the Region of Practical Interest (ROPE), it is robust to the scale of both the response variable and the predictors. However, similarly to its frequentist counterpart - the p-value, this index is not able to quantify evidence in favor of the null hypothesis.[2]
Relationship with p-value
The probability of direction has a direct correspondence with the frequentist one-sided p-value through the formula and to the two-sided p-value through the formula . Thus, a two-sided p-value of respectively .1, .05, .01 and .001 would correspond approximately to a pd of 95%, 97.5%, 99.5% and 99.95%.[5] The proximity between the pd and the p-value is in line with the interpretation of the former as an index of effect existence, as it follows the original definition of the p-value.[6][7]
Interpretation
The bayestestR package for R suggests the following rule of thumb guidelines:[8]
style="text-align: left; margin-left: auto; margin-right: auto; border: none;"| pd | p-value equivalence | Interpretation |
|---|---|---|
| 95% | p > .1 | Uncertain |
| 95% | p < .1 | Possibly existing |
| 97% | p .06 | Likely existing |
| 99% | p .02 | Probably existing |
| 99.9% | p .002 | Certainly existing |
See also
References
- ^ Makowski, Dominique; Ben-Shachar, Mattan; Lüdecke, Daniel (13 August 2019). "bayestestR: Describing Effects and their Uncertainty, Existence and Significance within the Bayesian Framework". Journal of Open Source Software. 4 (40): 1541. doi:10.21105/joss.01541.
- ^ a b Makowski, Dominique; Ben-Shachar, Mattan S.; Chen, S. H. Annabel; Lüdecke, Daniel (10 December 2019). "Indices of Effect Existence and Significance in the Bayesian Framework". Frontiers in Psychology. 10: 2767. doi:10.3389/fpsyg.2019.02767.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ^ Makowski, Dominique (5 February 2018). "The psycho Package: an Efficient and Publishing-Oriented Workflow for Psychological Science". The Journal of Open Source Software. 3 (22): 470. doi:10.21105/joss.00470.
- ^ Makowski, Dominique. "psycho - The Bayesian Framework". cran.r-hub.io. Retrieved 26 November 2021.
- ^ "BayestestR - Probability of Direction". https://easystats.github.io/bayestestR. Retrieved 26 November 2021.
{{cite web}}: External link in|website= - ^ Fisher, R. A. (1925). Statistical methods for research workers (11th ed. rev.). Edinburgh: Oliver and Boyd.
- ^ Cohen, Jacob (1994). "The earth is round (p < .05)". American Psychologist. 49 (12): 997–1003. doi:10.1037/0003-066X.49.12.997.
- ^ "Bayesian Reporting Guidelines". https://easystats.github.io/bayestestR. Retrieved 26 November 2021.
{{cite web}}: External link in|website=
External links
- bayestestR — an R package for computing Bayesian indices