PRELIMINARY-REPORT ON AN APPROACH TO TESTING FOR NORMALITY

The report is the introductory step to our investigation on joint probability distributions of crustal movements and geological parameters (basement depth, heat flow, seismicity and gravity anomalies) which will be carried out in the near future. Because of the remarkable role of the normal distribution, the working out of procedures testing for normality has been a continuing research subject of statisticians. Recently, Shapiro and Wilk (1965) and Shapiro et al. (1968) proposed a new test statistic and carried out a Monte Carlo comparative study with the known test statistics, and the result indicates superiority of their procedure from the test power point of view. The present report considers an approach to testing for normality which is related to the Shapiro-Wilk procedure. Also, the closed form of the test statistic is given. A brief historical outline of both the normal distribution theory and testing procedures is presented, making it of more methodological value, since the normal distribution is often involved in geodesy.