  We show that with the simple assumption of no correlation between the
Ly-alpha equivalent width and the UV luminosity of a galaxy, the observed
distribution of high redshift galaxies in an equivalent width - absolute UV
magnitude plane can be reproduced. We further show that there is no dependence
between Ly-alpha equivalent width and Ly-alpha luminosity in a sample of
Ly-alpha emitters. The test was expanded to Lyman-break galaxies and again no
dependence was found. Simultaneously, we show that a recently proposed lack of
large equivalent width, UV bright galaxies (Ando et al. 2006) can be explained
by a simple observational effect, based on too small survey volumes.
