Relation between the shape of population distribution and the robustness of four simple test statistics

The underlying theory upon which a great number of statistical procedures are based assumes that the variable or variables sampled are normally distributed. While there has been a good deal of theoretical research on the robustness of these procedures, the results seem not to have been set out in terms which the unsophisticated user of statistical methods can easily assimilate. The present paper, based on extensive computer simulation, aims at relating diagrammatically the shape of population to the robustness of the distribution of four simple statistics. A set of 29 Johnson SB and SU curves, several Pearaon and Weibull curves and some large-sample histograms have been used as populations. The results indicate the extent to which the population moment ratios √β1 and β2 determine the degree of robustness; charts rare provided which should help the user, if he has some knowledge of these two parameters, to decide whether the lack of robustness matters from the practical aspect with which he is concerned.