The objective of the analysis of the interobserver agreement and reliability is to provide information on the amount of error inherent in any rating system, knowing how to quantify this error it is possible to determine to what extent we can consider that the mentioned system is valid or not. Kappa coefficient is the most popular index for measuring agreement for discrete outcomes, due to its simplicity, applicability and intuitive explanation. Nevertheless, several statistical methods, models and extensions have been developed for this measure. Such is the special and novel case of the Bayesian analysis for kappa. For a long time, one of the limitations of the adoption of the Bayesian approach was to be able to put theory into practice, mainly those cases that presented analytically intractable join posterior distributions. With computational methods such as simulations of Monte Carlo using Markov Chains, this has been completely eliminated. That is why nowadays, Bayesian methods are used more frequently than ever in several fields of research. In this context, both the frequentist method and the Bayesian method were widely reviewed and applied in a real case in the field of medicine (glaucoma screening). Based on the results obtained, it was possible to compare the performance of the statistical methods, assess the degree of agreement among physicians and provide recommendations on future strategies for the glaucoma screening procedure.