3 ms·

I think we're actually in violent agreement here, but I just wasn't precise enough. Let me try again: p=0.05 means that one POSITIVE result in 20 is going

by lisper 3y ago

I think we're actually in violent agreement here, but I just wasn't precise enough. Let me try again: p=0.05 means that one POSITIVE result in 20 is going to be the result of chance and not causality In other words: if I have some kind of intervention or treatment, and that intervention or treatment produces some result in a test group relative to a control group with p=0.05, then the odds of getting that result simply by chance and not because the treatment or intervention actually had an effect are 5%. The practical effect of this is that there are two different ways of getting a p=0.05 result: 1. Find a treatment or intervention that actually works or 2. Test ~20 different (useless) interventions. Or test one useless intervention ~20 times. A single p=0.05 result in isolation is useless because there is no way to know which of the two methods produced it. This is why replication is so important. The odds of getting a p=0.05 result by chance is 5%. But the odds of getting TWO of them in sequential trials is 0.25%, and the odds of a positive result being the result of pure chance decrease exponentially with each subsequent replication.

thaumasiotes 3y ago
> Let me try again: > p=0.05 means that one POSITIVE result in 20 is going to be the result of chance and not causality No, you still didn't get it. In the example above, a full 100% of positive results, 20 out of every 20, are the result of chance and not causality. Your followup discussion is better, but your statement at the top doesn't work. (Note also that there is an interaction between p-threshold and sample size which guarantees that, if you're investigating an effect that your sample size is not large enough to detect, any statistically significant result that you get will be several times stronger than the actual effect. They're also quite likely to have the wrong sign.)
- lisper 3y ago
  > No, you still didn't get it. In the example above, a full 100% of positive results, 20 out of every 20, are the result of chance and not causality. Yep, you're right. I do think I understand this, but rendering it into words is turning out to be surprisingly challenging. Let me try this one more time: p=0.05 means that there is a 5% chance that any one particular positive result is due to chance. If you test a false hypothesis repeatedly, or test multiple false hypotheses, then 5% of the time you will get false positives (at p=0.05). However... > Imagine a hypothetical scientist that is fundamentally confused about something important, so all hypotheses they generate are false. Yet, using p=0.05, 5% of those hypotheses will be "confirmed experimentally". In that case, it is not 5% of the "experimentally confirmed" hypotheses that are wrong -- it is full 100%. This is not wrong, but it's a little misleading because you are presuming that all of the hypotheses being tested are false. If we're testing a hypothesis it's generally because we don't know whether or not it's true; we're trying to find out. That's why it's important to think of a positive result not as "confirmed experimentally" but rather as "not ruled out by this particular experimental result". It is only after failing to rule something out by multiple experiments that we can start to call it "confirmed". And nothing is ever 100% confirmed -- at best it is "not ruled out by the evidence so far".
  - hgsgm 3y ago
    You can't simply ignore the base rate, even if you don't know it. In a purely random world, 5% of experiments are false positives, at p=0.05. None are true positives. In a well ordered world with brilliant hypotheses, there are no false positives. If more than 5% of experiments show positive results at p=0.05, some of them are probably true, so you can try to replicate them with lower p. p=0.05 is a filter for "worth trying to replicate" (but even that is modulated by cost of replication vs value of result). The crisis in science is largely that people confuse "publishable" with "probably true". Anything "probably better then random guessing" is publishable to help other researchers, but that doesn't mean it's probably true.
    - lisper 3y ago
      > p=0.05 is a filter for "worth trying to replicate" Yes, I think that is an excellent way to put it. > The crisis in science is largely that people confuse "publishable" with "probably true". I would put it slightly differently: people conflate "published in a top-tier peer-reviewed journal" with "true beyond reasonable dispute". They also conflate "not published in a top-tier peer-reviewed journal" with "almost certainly false." But I think we're in substantial agreement here.
  - thaumasiotes 3y ago
    > I do think I understand this, but rendering it into words is turning out to be surprisingly challenging. A p-value of .05 means that, under the assumption that the null hypothesis you specified is true, you just observed a result which lies at the 5th percentile of the outcome space, sorted along some metric (usually "extremity of outcome"). That is to say, out of all possible outcomes, only 5% of them are as "extreme" as, or more "extreme" than, the outcome you observed. It doesn't tell you anything about the odds that any result is due to chance. It tells you how often the null hypothesis gives you a result that is "similar", by some definition, to the result you observed.
    - lisper 3y ago
      What do you think that "due to chance" means?

by lisper 3y ago

thaumasiotes 3y ago

> Let me try again: > p=0.05 means that one POSITIVE result in 20 is going to be the result of chance and not causality No, you still didn't get it. In the example above, a full 100% of positive results, 20 out of every 20, are the result of chance and not causality. Your followup discussion is better, but your statement at the top doesn't work. (Note also that there is an interaction between p-threshold and sample size which guarantees that, if you're investigating an effect that your sample size is not large enough to detect, any statistically significant result that you get will be several times stronger than the actual effect. They're also quite likely to have the wrong sign.)

lisper 3y ago
> No, you still didn't get it. In the example above, a full 100% of positive results, 20 out of every 20, are the result of chance and not causality. Yep, you're right. I do think I understand this, but rendering it into words is turning out to be surprisingly challenging. Let me try this one more time: p=0.05 means that there is a 5% chance that any one particular positive result is due to chance. If you test a false hypothesis repeatedly, or test multiple false hypotheses, then 5% of the time you will get false positives (at p=0.05). However... > Imagine a hypothetical scientist that is fundamentally confused about something important, so all hypotheses they generate are false. Yet, using p=0.05, 5% of those hypotheses will be "confirmed experimentally". In that case, it is not 5% of the "experimentally confirmed" hypotheses that are wrong -- it is full 100%. This is not wrong, but it's a little misleading because you are presuming that all of the hypotheses being tested are false. If we're testing a hypothesis it's generally because we don't know whether or not it's true; we're trying to find out. That's why it's important to think of a positive result not as "confirmed experimentally" but rather as "not ruled out by this particular experimental result". It is only after failing to rule something out by multiple experiments that we can start to call it "confirmed". And nothing is ever 100% confirmed -- at best it is "not ruled out by the evidence so far".
- hgsgm 3y ago
  You can't simply ignore the base rate, even if you don't know it. In a purely random world, 5% of experiments are false positives, at p=0.05. None are true positives. In a well ordered world with brilliant hypotheses, there are no false positives. If more than 5% of experiments show positive results at p=0.05, some of them are probably true, so you can try to replicate them with lower p. p=0.05 is a filter for "worth trying to replicate" (but even that is modulated by cost of replication vs value of result). The crisis in science is largely that people confuse "publishable" with "probably true". Anything "probably better then random guessing" is publishable to help other researchers, but that doesn't mean it's probably true.
  - lisper 3y ago
    > p=0.05 is a filter for "worth trying to replicate" Yes, I think that is an excellent way to put it. > The crisis in science is largely that people confuse "publishable" with "probably true". I would put it slightly differently: people conflate "published in a top-tier peer-reviewed journal" with "true beyond reasonable dispute". They also conflate "not published in a top-tier peer-reviewed journal" with "almost certainly false." But I think we're in substantial agreement here.
- thaumasiotes 3y ago
  > I do think I understand this, but rendering it into words is turning out to be surprisingly challenging. A p-value of .05 means that, under the assumption that the null hypothesis you specified is true, you just observed a result which lies at the 5th percentile of the outcome space, sorted along some metric (usually "extremity of outcome"). That is to say, out of all possible outcomes, only 5% of them are as "extreme" as, or more "extreme" than, the outcome you observed. It doesn't tell you anything about the odds that any result is due to chance. It tells you how often the null hypothesis gives you a result that is "similar", by some definition, to the result you observed.
  - lisper 3y ago
    What do you think that "due to chance" means?