Observational selection bias affecting the determination of the extragalactic distance scale

The influence of Malmquist bias on the studies of extragalactic distances is reviewed, with brief glimpses of the history from Kapteyn to Scott. Special attention is paid to two kinds of biases, for which the names Malmquist biases of the first and second kind are proposed. The essence of these biases and the situations where they occur are discussed. The bias of the first kind is related to the classical Malmquist bias (involving the ''volume effect''), while the bias of the second kind appears when standard candles are observed at different (true) distances, whereby magnitude limit cuts away a part of the luminosity function. In particular, study of the latter bias in distance indicators such as Tully Fisher, available for large fundamental samples of galaxies, allows construction of an unbiased absolute distance scale in the local galaxy universe where approximate kinematic relative distances can be derived. Such investigations, using the method of normalized distances or of the Spaenhauer diagram, support the linearity of the Hubble law and make it possible to derive an unbiased value of the Hubble constant.