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Astron. Astrophys. 343, 713-719 (1999)

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6. Application of the average bias formula

We are interested in seeing how large an effect on [FORMULA] cutoffs of different severities have. Table 1 shows the values of [FORMULA] ([FORMULA]) and the bias in [FORMULA] for different values of upper (lower) cutoff [FORMULA], and the corresponding completeness percentage of the sample.


Table 1. Bias in [FORMULA] due to p cutoffs. The upper sign in the [FORMULA] symbols refers to [FORMULA] while the lower sign refers to [FORMULA].

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 [FORMULA] and [FORMULA] 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.

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999