Testing normality

Abstract

Abstract In metrology, the normal distribution is often taken for granted, e. g. when evaluating the result of a measurement and its uncertainty, or when establishing the equivalence of measurements in key or supplementary comparisons. The correctness of this inference and subsequent conclusions is dependent on the normality assumption, such that a validation of this assumption is essential. Hypothesis testing is the formal statistical framework to do so, and this introduction will describe how statistical tests detect violations of a distributional assumption. In the metrological context we will advise on how to select such a hypothesis test, how to set it up, how to perform it and which conclusion(s) can be drawn. In addition, we calculate the number of measurements needed to decide whether a process departs from a normal distribution and quantify how sure one is about this decision then. These aspects are illustrated for the powerful Shapiro-Wilk test and by an example in legal metrology. For this application we recommend to perform 330 measurements. Briefly we also touch upon the issues of multiple testing and rounded measurements.