Monday, 18 May 2009

The tool I learned to use today, and what I discovered when I applied it

My life recently has reduced itself to not much more than working on the thesis in progress, or taking the occasional walk for exercise; I’ve even chosen to miss out on social events I would have otherwise attended in my push to “finish”. However, as I work I keep discovering new things I need to learn in the process. I once heard that the learning curve on a PhD project is exponential, and, truly, I believe it—it seems to me that I am learning ever so much more every day now in this very late stage of the project than I did in the early months of working on it (and, for the record, during those early months, I was astounded by just how very much I was learning compared to my prior rates of information acquisition).

One of this week’s new lessons was how to apply a t-test in an Excel spreadsheet. When my advisor gave me back chapter five, with comments and suggestions for improvement, one of the things he said was that the variation of some of the abundances for some of the trace elements in the monazite for the grains which grew in the Cambrian looked on the graph like they might, perhaps, vary by age of the grains. The “vary by age” we are talking here is very minor—these crystals grew ~505 Million years ago, give or take a handful of million years. How long did that growth period take? If it was fast it might have been just a couple million years, but if it was slow it could have taken tens of millions of years. In the latter case, it would be possible for there to be changes in the growing conditions (temperature/pressure) over the time period. If there were changes in the temperature and pressure during the metamorphic episode it is possible that during that period different minerals would be stable at different times during the event. It is known that how much of any given trace element is incorporated into monazite is based, in part, on what other minerals are growing or breaking down at the same time the monazite is growing. Since monazite tends to be a small mineral (generally <> 1 mm, and sometimes > 1 cm)) tend to out-compete it for any elements they are fond of if they are growing at the same time, or if the large mineral is breaking down, they tend to release trace elements, which the monazite can then incorporate into its own crystal structure.

Therefore, to test this, part of my day was spent going back to the results of my monazite analyses, sorting them by age to get all of the ones from the ~505 Million year old growing episode together, then sorting them back out into their individual samples again, then sorting each sample by first one, and then another trace element, then doing a t-test for each element to compare all of the analyses from a single sample which are high in that element with those which are low in that element. If the “t Stat” number reported is larger than the “t Critical two-tail” number then I can say that, yes, there is a statically valid difference in the ages of the two groups. However, for the samples from the first region I’ve tested, I can’t say that. Statically, the ages for those analyses high in these elements are indistinguishable from those which are low in those elements. Therefore, the factor which is more likely to effect how much of each of those trace elements wound up in the monazite is probably just a simple “how close was each grain of monazite to the other minerals which were either giving off, or taking up, those elements?”.

Having done all of that for this region, I next need to repeat the process for the other regions, write up the results (in less general terms!) in the thesis, and move on to the next task on the list…

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