Motivation: 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. Results: Starting from statistics that incorporate phylogenetic information only as independent sequence evolution models for each position of a multiple alignment, and extending this idea to a joint evolution model of two positions, we enhance the usual purely statistical methods (e.g. methods based on the Mutual Information statistic) with the use of phylogenetic information available in the sequences. In particular, we present a joint model based on the HKY evolution model, and consequently a X2 test of independence for two positions. A significant part of this work is devoted to some mathematical analysis of these methods. We tested these statistics on regions of 16S and 23S rRNA, and tRNA.