OK, there is a lot of interesting discussion and I accept that there may be some issues that are too tricky for me as a non-astronomer. I think that others are better to try and resolve those questions.

However I think that this is an interesting test because it is a new way of looking at it and directly tests big bang versus Arp and each has a specific outcome that is very clearly different.

Agreed that quasar definition must be a factor, but people are making catalogs based on some definitions. I think that such discussions should happen before making the catalogs. OK, you might agree with that but say it hasn't been done. In that case there needs to be agreement on what is definitely a quasar rather than a maybe. It should be a similar definition to what was used for quasars used by Arp when he did his earlier studies, because that is what we are testing. So any advice on how to achieve that would be most welcome.

Of course there are issues about how the universe develops and the changing nature of quasars over time. Both sides will agree that quasars are a stage of development but the details will be different.

For this proposal, I think it best to use relatively low redshift quasars that are relatively bright, but great care must be taken not to bias the results. If Arp is right that they are ejected from galaxies at much lower redshifts, then the galaxy sample can also be rather low redshift ones but with enough range to have the possibility of a sensible scatter diagram.

I think that the statistical problem of such a test are best solved by making a model for each of the alternative theories using Monte Carlo techniques and reasonable assumptions that are agreed by that side. Such data should be able to reproduce existing scatter diagrams and statistics about number of objects by redshift. Then the models are each used in the Monte Carlo test based on the two alternatives - line of sight coincidence for big bang and real association for Arp model to make scatter diagrams in advance of the test being done. The Arp test would need to allow for some true line of sight coincidences, but these should vary with the closeness of the limit set for separation between galaxy and quasar. In the Arp case the real separation does seem to be ~50 KPc so setting an angular limit that varies through 500 KPc, 200KPc, 100 KPc, 50 Kpc should show a steady progression from many to few line of sight objects.