Judicious application of a complementary set of sophisticated analytic techniques to large databases from human/machine anomalous in- teraction experiments can extract subtle structural features that might elude more simplistic analyses. The combination of a multi-factor analysis of vari- ance (ANOVA) with various subsidiary, ad hoc approaches suggested by the ANOVA or directly by the data, can establish an instructive hierarchy of salient physical and subjective parameters and illuminate some of their spe- cific details. In this particular study, the dominant finding is a significant cor- relation of anomalous effects with prescribed intentions of the human opera- tors, compounded of small contributions from many individuals across many experimental conditions. The grand concatenation, which includes all com- binations of successful and unsuccessful parameters or conditions, shows a chance probability for this correlation with intention on the order of 10 - 4 . The effect apparently is confined to non-deterministic devices; i.e., deter- ministic pseudo-random sources show no overall effect. The correlation with intention for non-deterministic sources alone has a chance probability of 10 - 6 . Beyond operator intention, most of the other technical, procedural, and subjective parameters explored show unimpressive contributions to the over- all variance, with a few notable exceptions that are clarified in the subsidiary analyses. For example, individual differences among operators are indicated, but there is a relatively normal distribution of effect sizes, within which a few participants are distinguished by consistent achievement over large databas- es. The temporal development of effect sizes shows a consistent pattern of initial success that declines but then recovers. There is essentially no evi- dence for a dependence of effect size on spatial or temporal separation, sup- porting other indications that ordinary physical variables have little impact on the anomalous interactions. In sum, although the composite ANOVA models explain less than 1% of total variance, implying very small and subtle effects, the analysis provides strong evidence that the anomalies are statisti- cally robust; they are not due to chance fluctuations, but are demonstrably correlated with definable subjective factors.