A Bayesian Approach for Wilcoxon Signed-Rank Test and Its Application to the Farmer’s Exchange Rate in Indonesia

Abstract

Wilcoxon Signed-Rank Test (WSRT) is a rank-based statistical nonparametric method to test two paired samples. Researchers often use a frequentist approach in testing by utilizing test statistics or p-values. This approach has limitations in providing information about the rejection of the alternative or null hypothesis. These limitations have spurred interest in Bayesian-based testing, known as the Bayes Factor. The advantage of the Bayesian approach is it can measure how much the data support one hypothesis over another. However, there is a problem of using Bayesian approach in WSRT, since there is no distribution of the rank implies no likelihood can be formed from the data rank. Van Doorn proposed a Bayesian approach for this test by using a latent normal approach, by modeling the data rank being come from latent variables that are normally distributed. The objective of this study is to test whether there is difference between farmer exchange rate 2021 and 2022 in Indonesia. We used Wilcoxon Signed Rank Test with Bayesian approach as given by Van Doorn. The test employs Bayes factor to make conclusion, by transforming the rank of data using latent variable that assuming follow normal distribution. The analysis was conducted by constructing a posterior population of difference ( ) of 475,000 using the Gibbs Sampling algorithm. It is obtained the values of Bayes Factor  is of 3076.07 and concluded that there is difference of farmer exchange rate in Indonesia between 2021 and 2022. This Bayes Factor indicates extreme evidence of a significant difference in the farmer exchange rate in Indonesia between 2021 and 2022.