GTest: a software tool for graphical assessment of empirical distributions’ Gaussianity

Abstract

In the present paper, the novel software GTest is introduced, designed for testing the normality of a user-specified empirical distribution. It has been implemented with two unusual characteristics; the first is the user option of selecting four different versions of the normality test, each of them suited to be applied to a specific dataset or goal, and the second is the inferential paradigm that informs the output of such tests: it is basically graphical and intrinsically self-explanatory. The concept of inference-by-eye is an emerging inferential approach which will find a successful application in the near future due to the growing need of widening the audience of users of statistical methods to people with informal statistical skills. For instance, the latest European regulation concerning environmental issues introduced strict protocols for data handling (data quality assurance, outliers detection, etc.) and information exchange (areal statistics, trend detection, etc.) between regional and central environmental agencies. Therefore, more and more frequently, laboratory and field technicians will be requested to utilize complex software applications for subjecting data coming from monitoring, surveying or laboratory activities to specific statistical analyses. Unfortunately, inferential statistics, which actually influence the decisional processes for the correct managing of environmental resources, are often implemented in a way which expresses its outcomes in a numerical form with brief comments in a strict statistical jargon (degrees of freedom, level of significance, accepted/rejected H0, etc.). Therefore, often, the interpretation of such outcomes is really difficult for people with poor statistical knowledge. In such framework, the paradigm of the visual inference can contribute to fill in such gap, providing outcomes in self-explanatory graphical forms with a brief comment in the common language. Actually, the difficulties experienced by colleagues and their request for an effective tool for addressing such difficulties motivated us in adopting the inference-by-eye paradigm and implementing an easy-to-use, quick and reliable statistical tool. GTest visualizes its outcomes as a modified version of the Q-Q plot. The application has been developed in Visual Basic for Applications (VBA) within MS Excel 2010, which demonstrated to have all the characteristics of robustness and reliability needed. GTest provides true graphical normality tests which are as reliable as any statistical quantitative approach but much easier to understand. The Q-Q plots have been integrated with the outlining of an acceptance region around the representation of the theoretical distribution, defined in accordance with the alpha level of significance and the data sample size. The test decision rule is the following: if the empirical scatterplot falls completely within the acceptance region, then it can be concluded that the empirical distribution fits the theoretical one at the given alpha level. A comprehensive case study has bee...

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