**2.3. Selection effects**

One characteristic feature of these plots is that at larger
distances the number of galaxies decreases. This phenomenon is
entirely due to the way the surveys are built: they are
flux-limited, therefore only the galaxies bright enough to have an
apparent magnitude exceeding the survey cutoff are detected. At
larger distances it is only possible to observe the intrinsically
most luminous galaxies. To account for this incompleteness in the
statistical analysis of these surveys, one needs to know the
selection function
(*r*),
which basically provides the
probability that a galaxy at a given distance *r* is included in
the sample. This is the radial selection function that is
usually estimated from the - previously calculated - luminosity
function, (*L*). The
luminosity function is defined by
the number density of galaxies in a given range of
intrinsic luminosity [*L*, *L* + *dL*],
(*L*)*dL*.
This function varies with
morphological type, environmental properties and redshift due to
galactic evolution. Traditionally it has been empirically fitted
to a Schechter function
[12]

(1) |

where *L*_{*} is a characteristic luminosity which
separates the faint galaxy range where the power-law with exponent
dominates Eq. 1 and the bright end where the number
density decreases exponentially.

Other selection effects affect the galaxy samples. Many of them are
directional. Some are due to the construction of the sample:
masks in given fields, fiber collisions in the spectrographs,
etc. In addition, the sky is not equally transparent to the
extragalactic light in all directions due to absorption of light
performed by the dust of the Milky Way. Since the shape of our own
Galaxy is rather flat, the more obscured regions are those with
low values of | *b*| (where *b* is the galactic latitude). This
effect has to be considered when computing the real brightness of
a galaxy, which therefore depends on the direction of the
line-of-sight. The best way to take this effect into account is to
consider the well defined maps of the distribution of galactic dust
[13].

For very deep samples, the absolute magnitude has to be estimated considering other adjustments like the K-correction, which takes into account that the luminosity of the galaxies at large redshift is detected at longer wavelength than actually was emitted.

Once the selection effects have been considered, the statistical analysis of the galaxy surveys are performed assigning to each galaxy a weight inversely proportional to the probability that the galaxy was included in the sample. A more clean solution is to consider volume-limited samples at the price of throwing away a huge amount of the collected data: At a given distance limit, one can easily calculate the absolute magnitude of a galaxy having the apparent magnitude limit of the survey. All galaxies intrinsically fainter that this absolute magnitude cutoff will be ignored in the volume-limited sample. An illustration of this procedure is shown in Fig. 3.