We investigated the triples distance as a measure of the distance betw
een two rooted bifurcating phylogenetic trees. The triples distance co
unts the number of subtrees of three taxa that are different in the tw
o trees. Exact expressions are given for the mean and variance of the
sampling distribution of this distance measure. Also, a normal approxi
mation is proved under the class of label-invariant models on the dist
ribution of trees. The theory is applied to the usage of the triples d
istance as a statistic for testing the null hypothesis that the simila
rities in two trees can be explained by independent random structures.
In an example, two phylogenies that describe the same seven species o
f chloroccalean zoosporic green algae are compared: one phylogeny base
d on morphological characteristics and one based on ribosomal RNA gene
sequence data.