Fig. 2

Schematic diagram illustrating the process of constructing a single Q tree. At each node, the covariate with the greatest value of the Q statistic is selected. The same covariate is allowed to be selected multiple times at downstream nodes. In each split, two nodes are formed according to the values of the covariate selected. The lower/upper M refers to the residual values in the lower/upper quantile region when using the residual method, or the lower/upper M samples in each pre-stratum when using the doubly-ranked method. The node will stop splitting when it meets any one of the stopping rules: (i) the split will cause the node size to be less than 1000, (ii) the Q-statistic value of the chosen covariate is less than 3.84 (the 95th percentile of a chi-squared distribution with one degree of freedom), or (iii) the maximum tree depth for the node is larger than 5