Statistics?
Dancing David,
thanks for the welcome!
My statistics knowledge is less than I would like but your comments:
- to say that a QSO has x probability of being in y area of the sky and that there is z chance that 4 objects would appear in y has intuitive appeal. It is not however a good use of population statistics. That would be making an argument that the members of the population would be evenly distributed through out the region, that they were spaced out on a regular basis.
Now assuming that this would be true, the stars that we could see would be allocated to the sky in a uniform sphere, if there was a ratio of x/y then for each section of y there would be x stars. So they would be distributed at the same regular intervals across the sky. So we would not have structure like constellation and other visible structures, so while you might determine a sample density per unit, it would be an error to construe the likelihood of a particular probability of a certain arrangement from the average population density.
Another analogy (and these are always full with peril) would be to look at the average populations density of human being on the landscape, these statistics are very common. But if you then found a city you could argue the low probability of the city occurring, if you assumed that all the human being were evenly spaced out, say that our city is a kilometer square and that the density if (.1 person/sq. km.) so if we had 10 people in our city you could falsely say that there was a (.1)^10 chance of this happening.
I have a hard time making sense of. It seems like you are stating that Arp has incorrectly assumed that QSOs and galaxies are evenly distributed; or he has incorrectly assumed that QSOs and galaxies are a "general" population.
If this is not the case, than how can we use statistical processes when discussing these populations at all? Does that mean we cannot make inferences about the galaxy population?
Or is it that Arp is making the wrong inferences. Aren't his claims similar to the following claim:
For stars of magnitudes 6-9, we find an approximately even distribution throughout the sky. However, we see a formation, Collinder 399, that looks curiously like a coathanger, a quite unnatural form. It would seem that the chances of this being a random occurrence is markedly low. Sure enough, there are few, if any other associations of this shape in the sky. And, as it turns out, this "random" arrangement is due to a close association of the brightest stars; i.e., they all formed at about the same time, in the same general region of space. Turns out they are a physically associated cluster.
To me, this line of reasoning is sound, but like I said my statistics are very rusty.
Basically, I think that the problem with your criticism of Arp's statistics is evident in your example regarding human population density: the odds of a high people density in a particular location would be astronomical,
if the density was a random occurrance, the high density is not random, the people are part of a city or association, and that is why the density is high.
That is exactly what Arp is trying to say: the probability of X number of QSO's being around a bright galaxy is astronomical, if this was truly a random occurance. Perhaps the occurance is not random; perhaps there is an association?
The odds of their being hundreds of kit-built planes at one time in a Oskosh Wisconsin are astronomical..unless their is an association! There is, believe it or not! No flawed statistics here!