The well-known Johnson system of distributions was developed by N. L. Johnson (1949). Slifker and Shapiro (1980) presented a criterion for choosing a member from the three distributional classes (SB,SL, and Sv) in the Johnson system to fit a set of data. The criterion is based on the value of a quantile ratio which depends on a specified positive z value and the parameters of the distribution. In this paper, we present some properties of the quantile ratio for various distributions and for some selected z values. Some comments are made on using the criterion for selecting a Johnson distribution to fit empirical data.