The largest angular size (LAS)-redshift(z) diagram has sometimes been used as an argument in favor of the cosmological interpretation of the apparent redshifts of quasars. It is important to establish whether or not the existence of the envelope is real or whether it arises because of some statistical selection effect. We have demonstrated that the observed behavior of the envelope of the LAS-z plot is a consequence of statistical effects and is just a reflection of the redshift distribution diagram, and that it has no intrinsic physical significance. Prior to our analysis, it was thought that the component size decreases with increasing redshift. Our analysis showed that if the the LAS is measured for a good number of large redshift quasars, some of them will show a large LAS. This has been confirmed at least for one quasar (Gearhart and Pact).