two things make a post

[kaberett]

1. I assume I have gone on at all of you who might be interested about how the PACE trial finding that Graded Exercise Therapy and CBT "cures" CFS/ME is a crock of shit? Just in case, it's a crock of shit, if it's not working for you the problem isn't you.

2. STATS QUESTION (because the last time I actually had to do any to pass an exam was circa summer 2008 and I have been resolutely ignoring the majority of it ever since): I have two datasets, one much larger than the other. For one (~2500 data points), the concentration ratio A/B is very uniform, makes a nice flat line when you plot it against B, *and also* This Other Quantity B' is also pretty uniform. For the second (~75 data points), the concentration ratio A/B varies over several orders of magnitudes, makes a nice *sloping* line when plotted against B, and there's also a lot of variation in B' (again, a few orders of magnitude). Is there... any useful way for me to say, in a scholarly fashion, "look, when A/B is uniform so is B', but when A/B isn't uniform B' isn't either", or...? (A/B doesn't have any straightforward correlation with B', it's the *range of variation* in both that I think might be correlated.)

Comments

[mdlbear]

What happens when you plot B vs. B'? Or A vs. B'?

Or make a 3-D scatterplot of A, B, and B'?

In any case it sounds as though there may be another variable involved.

[kaberett]

... oh good grief I completely forgot to mention that This Is Geochemistry, which means that A/B is, all else being equal, expected to be constant (as it is for the larger dataset) *in a way that just A or just B won't be* -- you're basically normalising one element to another to abstract the effects of "how much of the source rock has melted" and things like that.

SO. No, B vs B' doesn't show any correlation (which is a good thing in this context), and A vs B' just... isn't expected to have any relationship at all.

But A/B and B' might plausibly, because Geochemistry, but maybe I should ditch the abstraction and just... ask the actual question, though I'm not sure it would be more comprehensible.

[mdlbear]

Ah; that explains it. Don't know much about geochemistry; my last chem course in college was organic. But I know enough about geology to be dangerous (living near major faults and subduction zones will do that). I'm not sure it's relevant, but my father was a chemist.

So now I'm curious.

[mdlbear]

So am I correct in thinking that B' is actually the ratio of the two isotopes of B? Something like B"/B?

If that's the case, it might indeed be instructive to plot A/B against B', A/B against B" and A/B" against B".

Also, try doing some regression analysis to see what's correlated with what, and whether that's statistically significant.

[wolby]

Also trying to picture what's going on with the plots. If B' isn't independent of B (which I assume because of your naming convention), is there a way to write A/B in terms of A and B' instead? Should make it easier to tell what's going on.

Seconding @mdlbear's suggestion that you plot A vs B' (and B vs B' if I'm wrong about my assumption).

[kaberett]

OKAY SO I kind of forgot when asking this that "it's all geochemistry" and "volcanoes all the way down" were... important context...

The naming convention arises because I have element A and also element B. In addition to caring about elemental abundance, I care about the ratio of the two isotopes of B, and I have designated that ratio B' because it's... not... reaaaaaaaaaaally... independent...?

The thing is, if you just look at absolute concentration of A, or of B, you get A Bunch of confounding factors that are essentially impossible to deconvolve (including "we have no idea how much of the rock melted or what the actual source composition was") BUT, if elements A and B behave similarly during melting and crystallisation processes for the specific geological context... then you can normalise them to one another, remove the entire issue of absolute abundances, and get an elemental ratio that should be invariant unless Weird Shit Is Going On.

SO.

What I've actually got is that for one type of lavas, I'm seeing (as expected) constant A/B and a very uniform value of B'.

For the other -- smaller -- dataset, I'm seeing a big variation in A/B, which suggests that Weird Shit Is Going On in terms of melting processes, etc etc etc. I am ALSO seeing a lot of variation in B', the ratio of the two isotopes that make up element B. I am trying to work out whether there is any meaningful statistical test for "is there an actual correlation here or do I just get to wave my hands around qualitatively?" Because if A/B (which ought to be invariant) and B' (which is definitely uniform in contexts where A/B is invariant) are Actually Correlated then I get to start worrying about causation, and in turn get to start trying to wrap my head around a mechanism that could both fractionate A from B and fractionate iB from iiB.

ALL OF WHICH MEANS that "A vs B'" definitely won't (and indeed doesn't) show anything interpretable by itself, and B vs B' also doesn't show a correlation (which is good, for different reasons, but broadly because if the absolute abundance of B was a control on B' that would say Worrying Things about B' being completely unusable for the applications I'm trying to... use it for).

But, as I say, I had just... completely forgotten that geochemistry is A Bit Special about this.

[wolby]

Haha, that makes more sense! I should have suspected chemistry stuff, because I knew you were talking about geology. I loved my geology coursework, but chemistry remains A Mystery to me. I started writing a response that maybe went too far into statsland and was going to involve Diagrams, but I need to get back to work, so here's my simplified attempt. :)

The equation for a linear regression is A/B = interceptterm + slopeterm * B + errorterm. Math Happens, and your computer spits out values for interceptterm and slopeterm that minimize errorterm.

But the slope in your case is not just related to B, it's also potentially related to the ratio B' of the dataset. (Is this the same across all samples from the lava type, or also varies by data point?) One way to represent this is the following regression:

A/B = interceptterm + slopeterm * B + anotherinterceptterm * B' + anotherslopeterm * B' * B + error

You'll fit the whole dataset (both grouped together) to this equation. (Mechanics depend on what program you're using to do the regression; I can provide assistance if it's R.) The question that you can now mathematically pose is: does anotherslopeterm significantly differ from 0? (If you remember this wording: null hypothesis: anotherslopeterm = 0; alternate hypothesis: anotherslopeterm != 0.) In other words, does the ratio B' significantly affect the ratio A/B?

[wolby]

If this doesn't work for some reason (e.g. I misunderstood something about the data, or it violates another linear regression assumption) there are other possible tests I can think of, but linear regression is easier to do and understand, and the details you've provided so far are not incompatible with multiple linear regression.

[notasupervillain]

As the variability in A/B increases (i.e. higher standard deviation in A/B) the variability in B' also increases.

[kaberett]

Okay, that's some of what I was thinking, buuuuuut the standard deviation on each individual measurement stays more-or-less the same; it's just the overall variance. And overall variance pretty much just gives me "well, here's one blob that has one standard deviation, and here's another that has another", which is two points, which doesn't feel like much to hang a hypothesis off?

[notasupervillain]

Okay, change it to variance instead of standard deviation. Or add exactly what standard deviation you've measured in the paper. It makes sense to me, and I am a geochemist.

I'd be comfortable stating that as a hypothesis in a paper. I'd expect more data sets if you want to do more than leave it as a question for future research.

Unless you've got theory to back up your hypothesis?

[kaberett]

Right, but the thing is I fundamentally can't get more data sets: there are three relevant tectonic settings (divergent plate margins, convergent plate margins, and Weird Shit In The Middle Of Nowhere), and the interesting effect is showing up in one of them.

I can --

aha, and you've just edited, so now I can be a bit more specific in a way that might be useful ;)

tl;dr I'm looking at a specific stable isotope ratios in OIB vs MORB. My stable isotope ratio B' shows a whole heap of variance in OIB (where I've got ~75 samples; like, ~10 log units) but is +-1 unit in MORB (where I've got about 2500, as you might expect). "Invariant" ratio of the element-of-interest with a geochemically-similar element is in fact invariant for MORB, but shows a very coherent, very definite trend (against element-of-interest-B) for OIB.

So: ???

(I do have OIB samples from a good range of places/components -- Hawai'i/Iceland/Azores/St Helena in the literature, and Gough/Tristan/Helena/Rurutu/Tubuai/French Marquesas I've analysed myself -- but basically all localities cover basically the entire range of both B' and A/B, so whatever's going on looks pretty global.)

[notasupervillain]

Order of magnitude increases in variance between samples sounds legit. Assuming you've got a cohesive theory on what's causing the variance - it sounds like multiple mixing sources?