In this paper we show that strong statistical evidence has been availa
ble for many years showing that QSO redshifts in at least some cases a
re not caused by the expansion of the Universe. In a complicated world
the number of unexpected associations that can be subjected to statis
tical test is very large and somewhere among the entire ensemble of su
ch associations a few may seem of significance, if taken separately, w
hich are only chance effects, however, occasioned by the profusion of
cases in the ensemble. False associations of this kind show up readily
as new data become available, since the original chance effects are u
nlikely to be repeated in the new data. An example was an algebraic fo
rmula for the sunspot number which caused a considerable stir early in
the present century, the formula agreeing with sunspot numbers over m
any years with seemingly uncanny precision, only for the agreement to
disappear as soon as new sunspot numbers came along. This well-known s
tatistical trap cannot be claimed against the proposition that QSOs of
high redshifts are sometimes physically associated with nearby galaxi
es. This proposition has now been exposed to statistical test for almo
st thirty years, and it survives in new data just as well as in old da
ta. Additionally, a number of cases have come along with the years whe
re actual physical connections have been detected between QSOs and nea
rby galaxies. Six of these cases are discussed in detail in the presen
t paper. It is consistent with standard physics for redshifts to arise
from doppler motions and also in radiation emitted by matter in a gra
vitational field, as well as from the cosmological expansion of the Un
iverse. These other possibilities have been examined repeatedly over t
he years but have never been found to give convincing explanations for
the QSO-nearby galaxy associations described above. One is therefore
left with the nonstandard possibility that different samples of matter
can have different mass scales. No theory of how the QSO mass scale c
ould be different from the usual galaxy mass scale has hitherto been f
ound acceptable, with the consequence that most astrophysicists and co
smologists have felt justified in ignoring the evidence for anomalous
redshifts, the thought being that what is known to be impossible remai
ns impossible no matter how strong the evidence for it may be. The mai
n purpose of the present paper is to question this mode of thinking. W
e show how, consistent with the quasi steady-state cosmological theory
developed recently in a number of papers, it is possible for samples
of material of different ages to have different mass scales.