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 discuss the advantages of the T _ { c } and T _ { v } statistics over standard completeness tests , particularly the widely used \cal { V } / \cal { V } _ { max } test which assumes spatial homogeneity , and we demonstrate how our T _ { v } statistic can essentially be regarded as an improved , cumulative \cal { V } / \cal { V } _ { max } test which makes better use of the magnitude completeness information in a redshift survey .
Finally 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 of m _ { b _ { j } } = 20.00 mag .
and m _ { r } = 17.45 mag .
respectively , indicating there are no residual systematic effects within the photometry .
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 .