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CC BY-NC-ND 4.0 · Revista Urología Colombiana / Colombian Urology Journal 2022; 31(03): e130-e140
DOI: 10.1055/s-0042-1756171
Review Article | Artículo de Revisión

Frequentist and Bayesian Hypothesis Testing: An Intuitive Guide for Urologists and Clinicians

Pruebas de hipótesis frecuentista y bayesiana: Una Guía intuitiva para urólogos y clínicos
José Gaona 
1   Urology Research Group, Instituto Uromédica, Universidad de Santander, Bucaramanga, Colombia
,
Daniel Sánchez
1   Urology Research Group, Instituto Uromédica, Universidad de Santander, Bucaramanga, Colombia
,
Cesar González
1   Urology Research Group, Instituto Uromédica, Universidad de Santander, Bucaramanga, Colombia
,
Fabio González
1   Urology Research Group, Instituto Uromédica, Universidad de Santander, Bucaramanga, Colombia
,
Angélica Rueda
1   Urology Research Group, Instituto Uromédica, Universidad de Santander, Bucaramanga, Colombia
,
Sebastián Ortiz
1   Urology Research Group, Instituto Uromédica, Universidad de Santander, Bucaramanga, Colombia
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Abstract

Given the limitations of frequentist method for null hypothesis significance testing, different authors recommend alternatives such as Bayesian inference. A poor understanding of both statistical frameworks is common among clinicians. The present is a gentle narrative review of the frequentist and Bayesian methods intended for physicians not familiar with mathematics. The frequentist p-value is the probability of finding a value equal to or higher than that observed in a study, assuming that the null hypothesis (H0) is true. The H0 is rejected or not based on a p threshold of 0.05, and this dichotomous approach does not express the probability that the alternative hypothesis (H1) is true. The Bayesian method calculates the probability of H1 and H0 considering prior odds and the Bayes factor (Bf). Prior odds are the researcher's belief about the probability of H1, and the Bf quantifies how consistent the data is concerning H1 and H0. The Bayesian prediction is not dichotomous but is expressed in continuous scales of the Bf and of the posterior odds. The JASP software enables the performance of both frequentist and Bayesian analyses in a friendly and intuitive way, and its application is displayed at the end of the paper. In conclusion, the frequentist method expresses how consistent the data is with H0 in terms of p-values, with no consideration of the probability of H1. The Bayesian model is a more comprehensive prediction because it quantifies in continuous scales the evidence for H1 versus H0 in terms of the Bf and the posterior odds.

Resumen

Dadas las limitaciones del método de significancia frecuentista basado en la hipótesis nula, diferentes autores recomiendan alternativas como la inferencia bayesiana. Es común entre los médicos una comprensión deficiente de ambos marcos estadísticos. Esta es una revisión narrativa amigable de los métodos frecuentista y bayesiano dirigida quienes no están familiarizados con las matemáticas. El valor de p frecuentista es la probabilidad de encontrar un valor igual o superior al observado en un estudio, asumiendo que la hipótesis nula (H0) es cierta. La H0 se rechaza o no con base en un umbral p de 0.05, y este enfoque dicotómico no expresa la probabilidad de que la hipótesis alternativa (H1) sea verdadera. El método bayesiano calcula la probabilidad de H1 y H0 considerando las probabilidades a priori y el factor de Bayes (fB). Las probabilidades a priori son la creencia del investigador sobre la probabilidad de H1, y el fB cuantifica cuán consistentes son los datos con respecto a H1 y H0. La predicción bayesiana no es dicotómica, sino que se expresa en escalas continuas del fB y de las probabilidades a posteriori. El programa JASP permite realizar análisis frecuentista y bayesiano de una forma simple e intuitiva, y su aplicación se muestra al final del documento. En conclusión, el método frecuentista expresa cuán consistentes son los datos con H0 en términos de valores p, sin considerar la probabilidad de H1. El modelo bayesiano es una predicción más completa porque cuantifica en escalas continuas la evidencia de H1 versus H0 en términos del fB y de las probabilidades a posteriori.

Keywords

null hypothesis testing - bayesian analysis - Bayes factor - frequentist - statistical analysis - p-value - dichotomization - bayesian hypothesis testing - null hypothesis significance testing - JASP

Palabras Clave

prueba de hipótesis nula - análisis bayesiano - factor de Bayes - frecuentista - análisis estadístico - valor p - dicotomización - prueba de hipótesis bayesiana - prueba de significación de hipótesis nula - JASP

Financial Support

The authors declare they have received no financial support pertaining to the present article.




Publikationsverlauf

Eingereicht: 22. Juni 2022

Angenommen: 22. Juni 2022

Artikel online veröffentlicht:
28. September 2022

© 2022. Sociedad Colombiana de Urología. This is an open access article published by Thieme under the terms of the Creative Commons Attribution-NonDerivative-NonCommercial License, permitting copying and reproduction so long as the original work is given appropriate credit. Contents may not be used for commercial purposes, or adapted, remixed, transformed or built upon. (https://creativecommons.org/licenses/by-nc-nd/4.0/)

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