I couldn't begin to tell you [1]. It's not a 25% variation, once you've extrapolated from the samples by 10,000x (or whatever). The 25% inter-sample error was on a few replicas of teeny tiny measurements. The post-extrapolation error bars are so wide that they're meaningless.
The Smithsonian magazine article is garbage. Ignore it. The paper is saying that they see longitudinal trends in plastic bioaccumulation in various cadaver tissues, and this is plausible. But no, you don't have a plastic spoon in your head. That's just panic porn.
[1] Actually...I just asked Gemini and it reminded me that the expected variance of a draw from a distribution, scaled by factor C, should have a variance of the scaled sample distribution that grows with C^2. So, if we scale up the measurement by a factor of 10,000, we'd expect the variance of the scaled estimate to be proportional to 10,000^2.
I may be misunderstanding you, but it sounds like you're claiming that they had e.g. 10 tiny samples of tissue, that their measurements had an average 25% variation across those 10 samples, and that therefore the whole brain estimate (mass 10,000x that of a single sample) therefore has a much greater uncertainty. But doesn't the standard error of the mean get reduced by the square root of the number of samples? i.e. if you had 10 samples with 25% variation across samples, and you're taking their mean, the error of that mean should be 25% / sqrt(10) = 8%. And that should be the relative error for the scaled up whole-brain microplastic concentration as well. Or is there some other source of variation that I'm missing?
You're talking about reduction in statistical variance due to replication of measurement (and then averaging). I'm talking about what happens when they extrapolate from that value by a huge factor (which is what they've done, and the silly article does egregiously).
The paper isn't clear what they mean when they said "~25% within-sample coefficient of variation", so I can't directly address what you're asking, but it's tangential to the point I'm making. My naïve interpretation is that they did an ANOVA, and reported the within-group variance, or something similar.
All I'm saying in my footnote is that, whatever the final point estimate, scaling it by a factor of C will affect the variance of the final sample distribution by C^2. So for example, if you have an 8% variance on the measurement at ug/g, and you scale it by 1300 (for 1300g; what the interwebs tells me is the mass of a standard human brain), then you'd expect the variance of the scaled measurement to be 1300^2 * 8%.
That makes a ton of assumptions that probably don't hold in practice -- and I expect the real error to be larger -- but illustrates the point.
> If you then scale the setup up by 1000 (=> getting 5kg as expected value), then the variance scales to 1000^2 * 0.04 = 40000 g^2.
They didn't "scale the setup". They made a small-scale measurement, then extrapolated from that result by many orders of magnitude. They didn't grind up whole brains and measure the plastic content.
Imagine the experiment as a draw from a normal distribution (the distribution is irrelevant; it's just easier to visualize). You then multiply that sample by 10,000. What is the variance of the resulting sample distribution?
> What is the variance of the resulting sample distribution?
Relatively? The same. Yes it scales quadratically, but that is just because variance has such a weird unit.
Just consider standard deviation (which has the same physical unit as what you are measuring, and can be substituted for variance conceptually): This increases linearly when you scale up the sample.
An example:
Say you take 20 blood samples (5 ml), and find that they contain 4.5 ml water, with a standard deviation of 0.1 ml over your samples.
From that, your best guess for the whole human (5 liters, i.e. x1000) has to be 4.5 liters water, with standard deviation scaled up to 0.1 liters (or what would you argue for, and why?)
...so you are saying that the probability distribution indicates that there is a 50% probability that there more than a spoon's worth of plastic in our brain?
Evaluate based on both. Why remove any explanatory variables?
And for what it is worth, the paper itself has plenty of other interesting findings that OP fails to discuss or rebut at all. OP asks an LLM some very basic statistics questions, putting into question their ability to credibly apply and interpret the LLM's findings.
My interpretation of that evidence is that OP, a random internet commenter, just doesn't think it is credible that plastics are harmful to humans, and is grasping at plastic straws with cherry picked evidence and poor rebuttals to reach that "fact based" conclusion.
The Smithsonian magazine article is garbage. Ignore it. The paper is saying that they see longitudinal trends in plastic bioaccumulation in various cadaver tissues, and this is plausible. But no, you don't have a plastic spoon in your head. That's just panic porn.
[1] Actually...I just asked Gemini and it reminded me that the expected variance of a draw from a distribution, scaled by factor C, should have a variance of the scaled sample distribution that grows with C^2. So, if we scale up the measurement by a factor of 10,000, we'd expect the variance of the scaled estimate to be proportional to 10,000^2.