I would like some advice on the appropriate test to use for comparing many sample proportions. I'm looking at data from the fossil record, particularly survivorship at geologic stage boundaries. Here's a plot of the data:
At each stage boundary (illustrated above with red dots) we record the number of species present as a proportion of those that existed in the previous stage. So, for example, 571 out of 584 species survived across the boundary at t=185.
The full data is:
SV(t=195) = 531/553 = 0.960
SV(t=190) = 567/571 = 0.993
SV(t=185) = 574/584 = 0.983
SV(t=170) = 571/601 = 0.950
SV(t=165) = 471/713 = 0.660
SV(t=160) = 495/551 = 0.898
SV(t=155) = 661/683 = 0.968
SV(t=150) = 724/754 = 0.960
At t=165 there is a large decrease in survivorship corresponding to a mass extinction, but I am interested in the proportion at t=160, which looks to be lower than those at t=195, t=190, t=185, t=170, t=155 and t=150. How can I test for this?
H(0): SV(t=195) = SV(t=190) = SV(t=185) = SV(t=170) = SV(t=155) = SV(t=150) = SV(t=160)
H(a): SV(t=195) = SV(t=190) = SV(t=185) = SV(t=170) = SV(t=155) = SV(t=150) > SV(t=160)
I'm not very familiar with statistics, but my first idea was to sum the proportions of the "normal" stages (t=195, t=190, t=185, t=170, t=155 and t=150) and compare that value to the proportion at t=160 using a z-test of the difference of two proportions:
SV(t=195,t=190,t=185,t=170,t=155,t=150) =
H(0): SV(t=195,t=190,t=185,t=160,t=155) = SV(t=165)
H(a): SV(t=195,t=190,t=185,t=160,t=155) > SV(t=165)
And then compare the two to see if there is a statistically signficant difference in the two proportions (0.912 and 0.898). Is this a valid approach? Or is there some other method that would compare the proportion at t=195 to each of the other survivorship proportions at t=190, t=185 and so on and report if any were statistically anomalous?
Other things I'm aware of that might affect the result are the unequal time intervals (e.g. between t=185 and t=170), which could be controlled to a certain extent by combining certain shorter stages. The other problem I think exists is that I'm not sure the proportions are independent. The low survivorship at t=160 might be due to the mass extinction at t=165, for example. Is there a way to deal with these issues (a non-parametric test, possibly Mann-Whitney U from wikipedia-ing)?.
Sorry for the length and crappy LaTeX, I just started learning it 5 minutes ago.