Advocates of conditional combination have argued that testing for inco
ngruence between data partitions is an important step in data explorat
ion. Unless the partitions have had distinct histories, as in horizont
al gene transfer, incongruence means that one or more data partitions
support the wrong phylogeny. This study examines the relationship betw
een incongruence and phylogenetic accuracy using three statistical tes
ts of incongruence. These tests were applied to pairs of mitochondrial
DNA data partitions from two well-corroborated vertebrate phylogenies
. Of the three tests, the most useful was the incongruence length diff
erence test (ILD, also called the partition homogeneity test). This te
st distinguished between cases in which combining the data generally i
mproved phylogenetic accuracy (P > 0.01) and cases in which accuracy o
f the combined data suffered relative to the individual partitions (P
< 0.001). In contrast, in several cases, the Templeton and Rodrigo tes
ts detected highly significant incongruence (P < 0.001) even though co
mbining the incongruent partitions actually increased phylogenetic acc
uracy. All three tests identified cases in which improving the reconst
ruction model could improve the phylogenetic accuracy of the individua
l partitions.