Keywords: Bayesian Analysis, p-values, logistic regression, Bayesian logistic regression,

P-values are frequently used in public opinion research to determine the statistical significance of binary survey data (e.g., "yes" or "no" responses). This approach has received considerable criticism, as p-values can be overly sensitive to sample size, often misinterpreted, and do not consider prior knowledge or context. The limitations of p-values are particularly significant in public opinion research, where obtaining accurate and actionable insights is crucial for policy development and decision-making. Recently, Bayesian methods have been recognized as more robust analytical tools because they offer probabilistic interpretations of results and allow for integrating prior knowledge. This study aims to expand on the increasing use of Bayesian techniques in public opinion research and highlight their practical applications in analyzing binary survey data. In particular, this study investigates the limitations of p-values in binary survey data analysis and propose a Bayesian alternative, specifically Bayesian Logistic Regression (BLR), to address the limitations.
BLR is particularly suited for binary outcomes because it allows for the incorporation of prior knowledge, handles binary data effectively, and provides probabilistic interpretations of effect sizes. The analysis will follow a Bayesian workflow using the rstanarm package in R, which leverages Markov Chain Monte Carlo (MCMC) methods to estimate posterior distributions. The workflow includes specifying priors, conducting convergence diagnostics (e.g., Rhat and effective sample size), and performing posterior predictive checks to assess model fit.
The data for this study comes from a public opinion survey conducted by the Decision Support Center in Saudi Arabia. The survey collected responses from a random sample of 1300 participants, focusing on binary outcomes related to public opinion. The target population includes Saudi residents aged 18 and older, and the sampling approach ensures representation across key demographic and regional groups. Data were collected via structured phone interviews, and the questionnaire covered financial assistance among different income groups in Saudi Arabia. Sampling weights will be applied to ensure representativeness.
The analysis focuses on modeling binary outcomes from the survey data using BLR. The dependent variable is a binary indicator of "receiving financial assistance" or "ability to save money". The independent variable is income, categorized into three groups: high, middle, and low. The analysis will estimate posterior distributions for each parameter, assess convergence using Rhat and effective sample size, and evaluate model fit through posterior predictive checks. The results using Bayesian approach is expected to:
• Highlight significant effects that would be dismissed as non-significant under a p-value-based approach.
• Provide probabilistic interpretations of results, such as the probability that an effect is greater than zero.
• Improve model fit and predictive accuracy through the incorporation of prior knowledge.
By demonstrating the advantages of BLR, the findings will contribute to ongoing methodological debates in the public opinion research and provide a practical alternative for analyzing binary survey data. This approach has the potential to influence how public opinion surveys are analyzed and interpreted, leading to more informed decision-making in policy and research.