Quote (darkfire @ 23 May 2011 15:22)
Since there are people posting here who claim to have some background in the field, can someone link me to a research level paper with a decent statistical methodology section? If the actual reported results of these tests are based entirely on CLT normal approximations with nothing else, I'm going to have to rethink my confidence in carbon dating. At the very least, I would hope they do some nonparametric estimation to test the assumptions of the model and some kind of moment test to make sure the CLT approximations are valid.
Paul, I don't think your criticisms of the statistics here are particularly valid assuming everyone is doing their jobs. We've gotten fairly good at identifying flaws in model assumptions by using tools that don't depend on any assumptions (other than that some unknown probability distribution is in the background). If they did their work well, even small sample confidence intervals would be more than accurate enough to rule out any serious problems. There is a bound on the maximum possible error from the CLT approximations that people use to justify sample sizes of 30 or more being fairly good estimates. As to your criticisms about the constancy of parameters, again given the amount of data I assume they have collected, they could use nonparametrics (much stronger than CLT in terms of assumptions, but weaker in the convergence rate) to test whether or not the parameter values might have changed significantly over time. Again, I don't know anything about the empirical methodology, but in terms of the tests we're good at identifying those kinds of problems.
Fair warning, I don't know anything about/couldn't care less about anthropology.
I was hoping you would join in, you're a huge numbers guy, so your input is most appreciated.
Couple things to note: The assumptions of starting parameters and constancies over time is only one of the problems. Even if you had a million numbers that all did the same pattern (such as maybe 1000 years ago the half-life rate tripled and quadrupled for a few years), then you would expect a constant across all things, and not be able to determine a flaw in the dating from the results, because everything would be +/- that amount (that was that age or older). Potentially flawed formulas or assumptions always resulted in the same potentially flawed answers, whether it's 1 test, or a million.
But yes, the process by which these assessments are made is by the predetermined age, which is used to benchmark the end results, and discard anomalous results. I cannot definitively state that at this very second in time, that is how they are done (they may change their process at any moment, which is a great thing about science!), but as of college courses being taught regarding this very subject, this is part of the process by which samples are submitted, tested, and results returned. This is especially true for fossils, which the predetermined date is often determined by the rock layer it was found in. This is a problem, because the rock layers were defined by the fossils that occurred in them, creating a sort of circular logic. This is not always the case, of course, but does serve as but one example. Incidentally, afaik, no dating techniques work accurately on the rock layers themselves. Here is a quick link I found on the subject, but I encourage you to do your own studies on it further, and not implicitly trust internet articles at face value:
http://wiki.answers.com/Q/How_do_you_determine_the_age_of_a_sedimentary_rock_or_a_fossil_contained_within_it -- This clearly explains the circular logic I am referring to.
Again, even so, there are still the assumptions about the starting parameters, and what occurred between that period and now that may or may not have altered or skewed the test results. One would expect that if there were such things occurring in nature, they would have a linear effect on the entire sample, and likely all samples that exist at the given time, making discovering such shifts in the constants exceedingly difficult to discovery without direct observation and measurement of them occurring during our lifetimes.