Development of Excel Functions for the Shapiro-Wilk Test Based on Royston’s Algorithm

Abstract

As the goal of our research, we developed functions that can be used on an Excel spreadsheet, which are suitable for testing the normal distribution of a statistical population. Our functions use Royston's algorithm, which is an extension of the Shapiro-Wilk test, the strongest test for normality. Thus, the evaluation of a sample with between 4 and 2,000 elements can be carried out with approximate calculations so that we can decide on normality by calculating the significance level, avoiding the use of the critical values of the Shapiro-Wilk test given in the table. Evaluations on the Excel spreadsheet can be automated using functions, therefore providing a faster and more convenient technique than statistical program packages. The programming of the functions was provided by the Microsoft Excel Visual Basic for Applications service. By transforming the Royston formulas, a function was also created that gives the critical value of the test for any first-order error probability.