In article , Ray Tomes
writes:

dropping to values nearer the galaxy redshift at greater distance. Arp
interprets this as the quasars having been ejected from the spiral
galaxy along the axis in the matched pairs at various time intervals.

I once did a back-of-the-envelope calculation that if QSOs were really
ejected from M33 as Arp claims, then one should be able to DETECT THEIR
PROPER MOTION WITH VLBI. To my knowledge, no-one has tried this. This
would falsify his theory of ejection.

If a statistical study of the above claims was made with comprehensive
samples of galaxies and quasars by computer analysis and it yielded
extremely low probabilities (like say 10^-10) would cosmologists abandon
the big bang and cosmological red shift assumptions? If not, why not?

Not immediately. IF this transpired, it would be one argument against
the standard model, compared to several more in favour of it. If one
thus rejected the standard model, one would have a lot of explaining to
do as to why all the other arguments seem to work. So, IF this
transpired, one would probably first---following Occam's razor---look
for things one might have overlooked in this analysis.

To be fair, it is difficult to get observing time for Arp objects. On
the other hand, I think Arp would have been better off sticking to the
data rather than associating himself with very off-the-wall theoretical
explanations for his stuff. Also, he tends to play the "I've been
mistreated and misunderstood" angle too much, so perhaps one can't blame
those who steer clear of looking into his claims. (In one book, he goes
on and on about the opposition he has come up against, but the dust
jacket says he is "on the staff" of the Max Planck Institute for
astrophysics. If that's discrimination, then I'd like people to
discriminate against my astronomical work!)