Our results show that the null hypothesis can be rejected. Therefore, we adopt the alternative hypothesis and here discuss the resulting partial orders inferred from the data.
The data presented in Figures 4 to 8 can be interpreted in terms of partial orderings on the speed and quality performances of the fully-automated and hand-coded planners at each of the four problem levels. This can be done, at each level, simply by putting an ordering between pairs of planners from A to B when the Wilcoxon value for that pair is reported in the sub-column associated with A and is significant at the 0.001 level. The results are shown in Figures 9 to 12. In each of these figures sub-graphs associated with each of the four problem levels are identified. The presence of an arrow in a graph indicates that a statistically significant ordering exists. The absence of an arrow from A to B indicates that no statistically significant relationship between A and B was found at the corresponding problem level and therefore that no transitive ordering can depend on such a relationship.