6. Application of the average bias formula
We are interested in seeing how large an effect on cutoffs of different severities have. Table 1 shows the values of () and the bias in for different values of upper (lower) cutoff , and the corresponding completeness percentage of the sample.
Table 1. Bias in due to p cutoffs. The upper sign in the symbols refers to while the lower sign refers to .
In particular, if half of the galaxies are lost because of the upper cutoff (while there is no lower cutoff), formula (18) adopts a simple form, which gives a rough estimate of the bias for such distorted samples.
With representative values and this gives the bias -0.056, or distances underestimated by about 14 percent, in the average. Intuitively, one might have expected a more substantial influence of the p cutoff, knowing that the assumption of no p-selection is so fundamental for the inverse relation method.
© European Southern Observatory (ESO) 1999
Online publication: March 1, 1999