  We have assessed the significance of Tully and Verheijen's (1997) bimodal
Ursa Major Cluster spiral galaxy near-infrared surface brightness distribution,
focussing on whether this bimodality is simply an artifact of small number
statistics. A Kolmogorov-Smirnov style of significance test shows that the
total distribution is fairly represented by a single-peaked distribution, but
that their isolated galaxy subsample (with no significant neighbours within a
projected distance of around 80 kpc) is bimodal at the 96 per cent level. We
have also investigated the assumptions underlying the isolated galaxy surface
brightness distribution, finding that the (often large) inclination corrections
used in the construction of this distribution reduce the significance of the
bimodality. We conclude that the Ursa Major Cluster dataset is insufficient to
establish the presence of a bimodal near-infrared surface brightness
distribution: an independent sample of around 100 isolated, low inclination
galaxies is required to establish bimodality at the 99 per cent level.
