Probability Plotting Positions and Goodness of Fit for the Normal Distribution

This paper considers the problem of choosing a plotting position to use in constructing a normal probability plot. Previous recommendations have focused pri- marily on choosing a position so that the resulting plot will yield the best possible graphical estimates of either the standard deviation or the quantiles of the hypothe- sised distribution. In this paper, emphasis is placed on choosing a plotting position so that the resulting plot is best able to detect departures from normality. Seven plotting positions are compared using empirical power results for correlation coefficient test statistics that are calculated directly from probability plots. The comparisons indicate that correlation tests based on six of the plotting positions have almost identical power and that the choice of a plotting position depends primarily on ease of use.