Methods that predict the structure of molecules by looking for statistical correlation have been quite effective. Unfortunately, these methods often disregard phylogenetic information in the sequences they analyze. Here, we present a number of statistics for RNA molecular-structure prediction. Besides common pair-wise comparisons, we consider a few reasonable statistics for base-triple predictions, and present an elaborate analysis of these methods. All these statistics incorporate phylogenetic relationships of the sequences in the analysis to varying degrees, and the different nature of these tests gives a wide choice of statistical tools for RNA structure prediction.