Statistical Inference Procedure By the Information-Based Test and Its Application in Marine Climatology

Abstract

Objectives of ecological studies should drive all aspects of design. These objectives must include hypothesis testing and appropriate sample size. High level of unexplained variation is typical in many ecological studies and may lead to incorrect inference about the population. Choosing appropriate sample size is one key strategy to cope with unexplained variation. In this study, we aim to determine sample size which depends upon the information-based test and show the superiority of this approach over the likelihood ratio test. Particularly, we focused on finding appropriate sample size for testing the variance of the normal distribution and Rayleigh distribution. The power curves are obtained both for information-based test and the likelihood ratio test by the Monte Carlo simulations. We used wave height data to show how the inference procedure should follow both for the likelihood test and information-based test procedure. In agreement with the theoretical results of Janssen (2014) it is found that wave height obeys the Rayleigh distribution. Sample size determination for testing the variance of the normal distribution and Rayleigh distribution with different parameters is demonstrated for the fixed effect sizes.