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John_Maxwell_IV comments on Knowledge value = knowledge quality × domain importance - Less Wrong
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The quality of a belief is not linear in the number of participants in the study supporting it.
You're ignoring heavily diminishing returns from additional data points. In other words, to persuade me that studies with many participants really are a lot better, you'd have to do some math and show me that if I randomly sampled just a few study participants and inferred based on their results only, my inferences would frequently be wrong.
This seems pretty clearly not the case (see analysis in my reply to this comment).
Additionally, in domains like negotiation, I'd guess that decent-quality knowledge of many facts is more valuable than high-quality knowledge of just a few. Studies are a good way to get high-quality knowledge regarding a few facts, but not decent-quality knowledge regarding many. (Per unit effort.)
Testing something a bunch of times doesn't make it the thing you most need tested. (And some things may be hard to test cleanly.)
Although the win (expressed as precision of an effect size estimate) from upping the sample size n probably only goes as about √n, I think that's enough for gwern's quantitative point to go through. An RCT with a sample size of e.g. 400 would still be 10 times better than 4 self-experiments by this metric. (And this is leaving aside gwern's point about methodological quality. RCTs punch above their weight because random assignment allows direct causal inference.)
Where is the math for this?
I agree that methodology is important, but humans can often be good at inferring causality even without randomized controlled trials.
Edit: more thoughts on why I don't think the Bienaymé formula is too relevant here; see also.
http://en.wikipedia.org/wiki/Variance#Sum_of_uncorrelated_variables_.28Bienaym.C3.A9_formula.29
(Of course, any systematic bias stays the same no matter how big you make the sample.)
What steven0461 said. Square rooting both sides of the Bienaymé formula gives the standard deviation of the mean going as 1/√n. Taking precision as the reciprocal of that "standard error" then gives a √n dependence.
This is true, but we're also often wrong, and for small-to-medium effects it's often tough to say when we're right and when we're wrong without a technique that severs all possible links between confounders and outcome.
I'm too lazy to do a better analysis now, but just to provide the barest of intuitions:
Let's say a study with trillions of participants has shown that using Strategy A works better than not using Strategy A 80% of the time. I'm about to decide whether or not to use Strategy A, and unfortunately I don't know about the study. I poll three of my friends who have all done rigorous self-experiments. (Or maybe I've done three rigorous self-experiments myself.) All it takes is a pocket calculator to show that I have a 90% chance of correctly guessing whether I should use Strategy A: .2^3 + 3 * (.8.2.2) = .104. And obviously if I poll myself, based on a single past rigorous self-experiment, I'll have an 80% chance of getting it right.
(A better analysis would probably use the normal approximation for the binomial distribution, so we could see results for all sorts of parameters, but that would be a pain to write out with my voice recognition system.)
I suspect that scientific evidence is most useful on questions that are hard to decide (e.g. if Strategy A works 51% of the time; incidentally this sort of knowledge is also the most useless), or in cases where your degree of belief matters beyond just choosing whether or not to use a strategy (seems kind of rare).
This last point about degree of belief not mattering much could explain why Bayesian statistics didn't catch on as well as frequentist statistics initially: most of the time, your exact degree of belief doesn't matter and you just need to decide whether or not to do something.
You're making a massive assumption: that self-experimentation is not biased worse than regular clinical trials by things like selection effects. This is what I mean by methodological concerns making each self-experiment far far less than n=1. I mean, look at OP - from the sound of it, the friend did not report their results anywhere (perhaps because they were null?). Bingo, publication effect. People don't want to discuss null effects, they want to discuss positive results. I've seen this first-hand with dual n-back, among others, where I had trouble eliciting the null results even though they existed.
Given this sort of bias and zero effort on self-experimenters' part to counter it, yes, you absolutely could do far worse than random by sampling 1000 self-experimenters compared to 1000 clinical trial participants! This is especially true for highly variable stuff like sleep, where you can spot any trend you like in all the noise - compare the dramatic confident anecdotes collected by Seth Roberts about vitamin D at night based on purely subjective retrospective recall of <10 nights to my actual relatively moderate findings based on 40 nights of Zeo data.
(I actually have a little demonstration that someone is engaging in considerable confirmation bias, but I'm not done yet. I should be able to post the result in early May.)
I don't necessarily disagree with you on any of this. Looks to me like we are talking past each other a little bit.
Something about your rough model disagrees with me (in addition to the stuff in gwern's comment). Tentatively I'd put my finger on strategies like your hypothetical strategy A being rarer than they look. I think it's uncommon for a prospective lifestyle change to simultaneously
(Edited to add "be" to bullet point 2.)
Well obviously you have to decide on a case-by-case basis whether Real Science is necessary, but the butter mind thing is looking pretty good:
http://quantifiedself.com/2011/01/results-of-the-buttermind-experiment/
Would you wait for a real study before trying this?
http://lesswrong.com/lw/ba6/alternate_card_types_for_anki/
W. T. F! ?
A half stick of butter every day makes you smarter - and in contrast to an equivalent amount of other saturated fats? That's really rather surprising. I would like to see more research on that. Because it is kind of awesome.
To be sure. I don't think my line of argument should shut the door on self-experimentation. I'd just focus on low-risk, low-effort interventions as candidates. (Otherwise I'm likely to end up with more high-risk/high-effort false positives than I'd like.)
So it is! When I saw the original Seth Roberts blog post my reaction was to write it off as a probable fluke. The fact that it seems to replicate in a randomized trial with n = 45 makes me much more interested, especially as the relative speed-up from the butter remained at about 5% (suggesting Seth's original result wasn't just a high/low outlier). I'd have chosen a different experimental design, and I'll have to take a look at the raw data to convince myself of the analysis, but it seems promising.
As for the Anki thing, I probably wouldn't wait! It's the sort of low-effort, low-risk intervention that's best for self-experimentation.