7 ms·

Well, it still tells us something. What are the upper and lower bounds of whole brain microplastic content, given that 25% variation?

timr 2y ago
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.
- drawkward 2y ago
  Why yes, i think i will believe the random internet commenter.
  - LoganDark 2y ago
    Practically every internet commenter is random.
    - drawkward 2y ago
      Which is fine in plenty of contexts. Rebutting this particular article? Nah.
      - robertlagrant 2y ago
        Evaluate things based on reasoning, not source.
        drawkward 2y ago
        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.
        robertlagrant 2y ago
        > 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. So what? If some things haven't been discussed or rebutted, then just say that the argument is incomplete for those reasons and move on.
- edouard-harris 2y ago
  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?
  - timr 2y ago
    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.
    - myrmidon 2y ago
      I think there is some kind of mixup, you can not scale up the variance percentages quadratically: If you do a small-scale measurement, say you get result of 5g, with a standard deviation of 0.2g. That means the variance is 0.04 g^2. 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. BUT the standard deviation is still 200g. The relative uncertainty is NOT increasing quadratically! (another sanity check: if you change the units by a factor of 1000, your variance must not increase, relatively). But maybe I misunderstood your point?
- drawkward 2y ago
  ...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?

timr 2y ago

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.

drawkward 2y ago
Why yes, i think i will believe the random internet commenter.
- LoganDark 2y ago
  Practically every internet commenter is random.
  - drawkward 2y ago
    Which is fine in plenty of contexts. Rebutting this particular article? Nah.
    - robertlagrant 2y ago
      Evaluate things based on reasoning, not source.
      - drawkward 2y ago
        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.
        robertlagrant 2y ago
        > 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. So what? If some things haven't been discussed or rebutted, then just say that the argument is incomplete for those reasons and move on.
edouard-harris 2y ago
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?
- timr 2y ago
  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.
  - myrmidon 2y ago
    I think there is some kind of mixup, you can not scale up the variance percentages quadratically: If you do a small-scale measurement, say you get result of 5g, with a standard deviation of 0.2g. That means the variance is 0.04 g^2. 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. BUT the standard deviation is still 200g. The relative uncertainty is NOT increasing quadratically! (another sanity check: if you change the units by a factor of 1000, your variance must not increase, relatively). But maybe I misunderstood your point?
drawkward 2y ago
...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?