A statistical selection effect that arises in astronomical surveys that are complete to some apparent magnitude limit. At large distances from the observer, only objects that are intrinsically luminous can be seen. Nearer the observer, objects with average or below-average luminosity can also be seen. The statistical properties of the sample therefore depend on distance from the observer in a complicated way. This form of bias, first described in 1924 by the Swedish astronomer Karl Gunnar Malmquist (1893–1982), can be avoided by forming a more restricted volume-limited sample.

Nowadays, the term Malmquist bias is often used to describe the systematic bias on a measured quantity due to random observational errors. For example, random errors in magnitude measurements will lead to an overestimate of the number of galaxies to a given magnitude limit, because there are more galaxies fainter than the limit which are scattered into the sample by measurement errors than there are galaxies brighter than the limit which are scattered out. A random measurement error thus leads to a systematic bias.