Inferring the allometric growth coefficient of juvenile African mud catfish, Clarias gariepinus (Burchell, 1822), using Bayesian and Frequentist regression models

Abstract

Statistics is essential in biological and ecological scientific research. However, the default Frequentist statistics based on p-value and null hypothesis testing is often misused and misinterpreted, hence causing reproducible crises. The p-value concept deserved further examination because it has been irretrievably lost. Therefore, there is dire need for reform in the default Frequentist statistics as practiced by researchers because of the perils of p-values. Bayesian statistics, using the tools of Bayes Factors and posterior distributions derived from priors and likelihood function; rooted in Bayes’ Theorem is one of the suggested alternatives. Frequentist (least square) and Bayesian (specifying uniform Jeffreys-Zellner-Siow prior, r-scale =0.35) regression models, a standard statistical protocol in fisheries were applied to determine the allometric growth coefficient based on length (mm) and weight (g) measurements of juvenile African mud catfish, Clarias gariepinus from Epe Lagoon. The growth coefficient, b=3.20, 95% Confidence Interval [3.07, 3.34], t(96)=47.55, p<0.001 was significant with 96% explanatory power (R²=0.96).While Bayesian method, with 96% explanatory power (R²=0.96), also estimated, b=3.20, (with Credible Interval between 3.06 and 3.32). The Bayes Factor (>100) suggested the data is more plausible under the alternative model than the null model, but p-value cannot quantify evidence in support of alternative hypothesis, since p-value can only reject or fail to reject a null hypothesis. These findings suggested that juvenile C. gariepinus thrived in Epe Lagoon. Therefore, Bayesian inference is a robust substitute for Frequentist regression model in fisheries.