Probability-Probability Plots - Categorized

In this graph, you can visually check for the fit of a theoretical distribution to the observed data by examining each probability-probability plot (also called Probability Plot, see also Probability-Probability Plots ) for the respective level of the grouping variable (or user-defined subset of data). In probability-probability plots (or P-P plots for short) the observed cumulative distribution function is plotted against the theoretical cumulative distribution function. As in the Categorized Quantile-Quantile plot , the values of the respective variable are first sorted into ascending order. The ith observation is plotted against one axis as i/n (i.e., the observed cumulative distribution function), and against the other axis as F(x(i)), where F(x(i)) stands for the value of the theoretical cumulative distribution function for the respective observation x(i). If the theoretical cumulative distribution approximates the observed distribution well, then all points in this plot should fall onto the diagonal line. One component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).