Goodness-of-fit tests for rating scale data: Applying the minimum chi-square method

Abstract

This paper discusses the concept of goodness-of-fit tests for 5-point rating scale data. Major problems of such tests include the lack of formulation of parameter estimates needed to run the tests, and the lack of computer capabilities for major statistical packages. We address these by implementing the minimum chi-square method. Steps for carrying out this method are outlined. Results of fitting 484 5-point Likert scale variables from diverse Management and Marketing surveys are fitted to normal, lognormal, beta, gamma, and Weibull distributions. Results show, among other things, that some continuous distribution is not an unreasonable fit for 49% tested.