  We have extended and improved the statistical test recently developed by
Rauzy for assessing the completeness in apparent magnitude of
magnitude-redshift surveys. Our improved test statistic retains the robust
properties -- specifically independence of the spatial distribution of galaxies
within a survey -- of the $T_c$ statistic introduced in Rauzy's seminal paper,
but now accounts for the presence of both a faint and bright apparent magnitude
limit. We demonstrate that a failure to include a bright magnitude limit can
significantly affect the performance of Rauzy's $T_c$ statistic. Moreover, we
have also introduced a new test statistic, $T_v$, defined in terms of the
cumulative distance distribution of galaxies within a redshift survey. These
test statistics represent powerful tools for identifying and characterising
systematic errors in magnitude-redshift data. We apply our completeness test to
three major redshift surveys: The Millennium Galaxy Catalogue (MGC), The Two
Degree Field Galaxy Redshift Survey (2dFGRS), and the Sloan Digital Sky Survey
(SDSS). We confirm that MGC and SDSS are complete up to the published (faint)
apparent magnitude limit Furthermore, we show that, unless a bright limit is
included for 2dFGRS, the data-set displays significant incompleteness at
magnitudes brighter than the published limit of $m_{b_{j}}=19.45$ mag.
