With the thresholds from physics, we’d still be figuring out if penicillin really, actually kills certain bacteria (somewhat hyperbolic, 5 sigma ~ 1 in 3.5 million).
0.05 is a practical tradeoff, for supposed Bayesians, it is still much too strict, not too lax.
I for one think that 0.05 is way too lax (other than for the purposes of seeing whenever it is worth it to conduct a bigger study and other such value-of-information related uses) and 0.05 results require rather carefully constructed meta-study to interpret correctly. Because a selection factor of 20 is well within the range attainable by dodgy practices that are almost impossible to prevent, and even in the absence of the dodgy practices, selection due to you being more likely to hear of something interesting.
I can only imagine considering it too strict if I were unaware of those issues or their importance (Bayesianism or not)
This goes much more so for weaker forms of information, such as “Here’s a plausible looking speculation I came up with”. To get anywhere with that kind of stuff one would need to somehow account for the preference towards specific lines of speculation.
edit: plus, effective cures in medicine are the ones supported by very very strong evidence, on par with particle physics (e.g. the same penicillin killing bacteria, you have really big sample sizes when you are dealing with bacteria). The weak stuff—antidepressants for which we don’t know if they lower or raise the risk of the suicide, and are uncertain whenever the effect is an artefact from using in any way whatsoever a depression score that includes weight loss and insomnia as symptoms when testing a drug that causes weight gain and sleepiness.
I think it is mostly because priors for finding a strongly effective drug are very low, so when large p-values are involved, you can only find low effect, near-placebo drugs.
edit2: Other issue is that many studies are plagued by at least some un-blinding that can modulate the placebo effect. So, I think a threshold on the strength of the effect (not just p-value) is also necessary—things that are within the potential systematic error margin from the placebo effect may mostly be a result of systematic error.
edit3: By the way, note that for a study of same size, stronger effect will result in much lower p-value, and so a higher standard on p-values does not interfere with detection of strong effects much. When you are testing an antibiotic… well, the chance probability of one bacterium dying in some short timespan may be 0.1, and with antibiotic at a fairly high concentration, 99.99999… . Needless to say, a dozen bacteria put you far beyond the standards from the particle physics, and a whole poisoned petri dish makes point moot, with all the unconfidence coming from the possibility of killing the bacteria in some other way.
It probably is too lax. I’d settle for 0.01, but 0.005 or 0.001 would be better for most applications (i.e—where you can get it). We have have the whole range of numbers between 1 in 25 and 1 in 3.5 million to choose from, and I’d like to see an actual argument before concluding that the number we picked mostly from historical accident was actually right all along.
Still, a big part of the problem is the ‘p-value’ itself, not the number coming after it. Apart from the statistical issues, it’s far too often mistaken for something else, as RobbBB has pointed out elsewhere in this thread.
0.05 is a practical tradeoff, for supposed Bayesians, it is still much too strict, not too lax.
No, it isn’t. In an environment where the incentive to find a positive result in huge and there are all sorts of flexibilities in what particular results to report and which studies to abandon entirely, 0.05 leaves far too many false positives. I really does begin to look like this. I don’t advocate using the standards from physics but p=0.01 would be preferable.
Mind you, there is no particularly good reason why there is an arbitrary p value to equate with ‘significance’ anyhow.
Well, I would find it really awkward for a Bayesian to condone a modus operandi such as “The p-value of 0.15 indicates it is much more likely that there is a correlation than that the result is due to chance, however for all intents and purposes the scientific community will treat the correlation as non-existent, since we’re not sufficiently certain of it (even though it likely exists)”.
Similar to having choice of two roads to go down, one of which leads into the forbidden forest. Then saying “while I have decent evidence which way goes where, because I’m not yet really certain, I’ll just toss a coin.” How many false choices would you make in life, using an approach like that? Neglecting your duty to update, so to speak. A p-value of 0.15 is important evidence. A p-value of 0.05 is even more important evidence. It should not be disregarded, regardless of the perverse incentives in publishing and the false binary choice (if (p<=0.05) correlation=true, else correlation=false). However, for the medical community, a p-value of 0.15 might as well be 0.45, for practical purposes. Not published = not published.
This is especially pertinent given that many important chance discoveries may only barely reach significance initially, not because their effect size is so small, but because in medicine sample sizes often are, with the accompanying low power of discovering new effects. When you’re just a grad student with samples from e.g. 10 patients (no economic incentive yet, not yet a large trial), unless you’ve found magical ambrosia, p-values may tend to be “insignificant”, even of potentially significant breakthrough drugs .
Better to check out a few false candidates too many than to falsely dismiss important new discoveries. Falsely claiming a promising new substance to have no significant effect due to p-value shenanigans is much worse than not having tested it in the first place, since the “this avenue was fruitless” conclusion can steer research in the wrong direction (information spreads around somewhat even when unpublished, “group abc had no luck with testing substances xyz”).
IOW, I’m more concerned with false negatives (may never get discovered as such, lost chance) than with false positives (get discovered later on—in larger follow-up trials—as being false positives). A sliding p-value scale may make sense, with initial screening tests having a lax barrier signifying a “should be investigated further”, with a stricter standard for the follow-up investigations.
Well, I would find it really awkward for a Bayesian to condone a modus operandi such as “The p-value of 0.15 indicates it is much more likely that there is a correlation than that the result is due to chance, however for all intents and purposes the scientific community will treat the correlation as non-existent, since we’re not sufficiently certain of it (even though it likely exists)”.
And this is a really, really great reason not to identify yourself as “Bayesian”. You end up not using effective methods when you can’t derive them from Bayes theorem. (Which is to be expected absent very serious training in deriving things).
Better to check out a few false candidates too many than to falsely dismiss important new discoveries
Where do you think the funds for testing false candidates are going to come from? If you are checking too many false candidates, you are dismissing important new discoveries. You are also robbing time away from any exploration into the unexplored space.
edit: also I think you overestimate the extent to which promising avenues of research are “closed” by a failure to confirm. It is understood that a failure can result from a multitude of causes. Keep in mind also that with a strong effect, you have quadratically better p-value for the same sample size. You are at much less of a risk of dismissing strong results.
Well, I would find it really awkward for a Bayesian to condone a modus operandi such as “The p-value of 0.15 indicates it is much more likely that there is a correlation than that the result is due to chance, however for all intents and purposes the scientific community will treat the correlation as non-existent, since we’re not sufficiently certain of it (even though it likely exists)”.
The way statistically significant scientific studies are currently used is not like this. The meaning conveyed and the practical effect of official people declaring statistically significant findings is not a simple declaration of the Bayesian evidence implied by the particular statistical test returning less than 0.05. Because of this, I have no qualms with saying that I would prefer lower values than p<0.05 to be used in the place where that standard is currently used. No rejection of Bayesian epistemology is implied.
That’s what multiple testing correction is for.
With the thresholds from physics, we’d still be figuring out if penicillin really, actually kills certain bacteria (somewhat hyperbolic, 5 sigma ~ 1 in 3.5 million).
0.05 is a practical tradeoff, for supposed Bayesians, it is still much too strict, not too lax.
I for one think that 0.05 is way too lax (other than for the purposes of seeing whenever it is worth it to conduct a bigger study and other such value-of-information related uses) and 0.05 results require rather carefully constructed meta-study to interpret correctly. Because a selection factor of 20 is well within the range attainable by dodgy practices that are almost impossible to prevent, and even in the absence of the dodgy practices, selection due to you being more likely to hear of something interesting.
I can only imagine considering it too strict if I were unaware of those issues or their importance (Bayesianism or not)
This goes much more so for weaker forms of information, such as “Here’s a plausible looking speculation I came up with”. To get anywhere with that kind of stuff one would need to somehow account for the preference towards specific lines of speculation.
edit: plus, effective cures in medicine are the ones supported by very very strong evidence, on par with particle physics (e.g. the same penicillin killing bacteria, you have really big sample sizes when you are dealing with bacteria). The weak stuff—antidepressants for which we don’t know if they lower or raise the risk of the suicide, and are uncertain whenever the effect is an artefact from using in any way whatsoever a depression score that includes weight loss and insomnia as symptoms when testing a drug that causes weight gain and sleepiness.
I think it is mostly because priors for finding a strongly effective drug are very low, so when large p-values are involved, you can only find low effect, near-placebo drugs.
edit2: Other issue is that many studies are plagued by at least some un-blinding that can modulate the placebo effect. So, I think a threshold on the strength of the effect (not just p-value) is also necessary—things that are within the potential systematic error margin from the placebo effect may mostly be a result of systematic error.
edit3: By the way, note that for a study of same size, stronger effect will result in much lower p-value, and so a higher standard on p-values does not interfere with detection of strong effects much. When you are testing an antibiotic… well, the chance probability of one bacterium dying in some short timespan may be 0.1, and with antibiotic at a fairly high concentration, 99.99999… . Needless to say, a dozen bacteria put you far beyond the standards from the particle physics, and a whole poisoned petri dish makes point moot, with all the unconfidence coming from the possibility of killing the bacteria in some other way.
It probably is too lax. I’d settle for 0.01, but 0.005 or 0.001 would be better for most applications (i.e—where you can get it). We have have the whole range of numbers between 1 in 25 and 1 in 3.5 million to choose from, and I’d like to see an actual argument before concluding that the number we picked mostly from historical accident was actually right all along. Still, a big part of the problem is the ‘p-value’ itself, not the number coming after it. Apart from the statistical issues, it’s far too often mistaken for something else, as RobbBB has pointed out elsewhere in this thread.
No, it isn’t. In an environment where the incentive to find a positive result in huge and there are all sorts of flexibilities in what particular results to report and which studies to abandon entirely, 0.05 leaves far too many false positives. I really does begin to look like this. I don’t advocate using the standards from physics but p=0.01 would be preferable.
Mind you, there is no particularly good reason why there is an arbitrary p value to equate with ‘significance’ anyhow.
Well, I would find it really awkward for a Bayesian to condone a modus operandi such as “The p-value of 0.15 indicates it is much more likely that there is a correlation than that the result is due to chance, however for all intents and purposes the scientific community will treat the correlation as non-existent, since we’re not sufficiently certain of it (even though it likely exists)”.
Similar to having choice of two roads to go down, one of which leads into the forbidden forest. Then saying “while I have decent evidence which way goes where, because I’m not yet really certain, I’ll just toss a coin.” How many false choices would you make in life, using an approach like that? Neglecting your duty to update, so to speak. A p-value of 0.15 is important evidence. A p-value of 0.05 is even more important evidence. It should not be disregarded, regardless of the perverse incentives in publishing and the false binary choice (if (p<=0.05) correlation=true, else correlation=false). However, for the medical community, a p-value of 0.15 might as well be 0.45, for practical purposes. Not published = not published.
This is especially pertinent given that many important chance discoveries may only barely reach significance initially, not because their effect size is so small, but because in medicine sample sizes often are, with the accompanying low power of discovering new effects. When you’re just a grad student with samples from e.g. 10 patients (no economic incentive yet, not yet a large trial), unless you’ve found magical ambrosia, p-values may tend to be “insignificant”, even of potentially significant breakthrough drugs .
Better to check out a few false candidates too many than to falsely dismiss important new discoveries. Falsely claiming a promising new substance to have no significant effect due to p-value shenanigans is much worse than not having tested it in the first place, since the “this avenue was fruitless” conclusion can steer research in the wrong direction (information spreads around somewhat even when unpublished, “group abc had no luck with testing substances xyz”).
IOW, I’m more concerned with false negatives (may never get discovered as such, lost chance) than with false positives (get discovered later on—in larger follow-up trials—as being false positives). A sliding p-value scale may make sense, with initial screening tests having a lax barrier signifying a “should be investigated further”, with a stricter standard for the follow-up investigations.
And this is a really, really great reason not to identify yourself as “Bayesian”. You end up not using effective methods when you can’t derive them from Bayes theorem. (Which is to be expected absent very serious training in deriving things).
Where do you think the funds for testing false candidates are going to come from? If you are checking too many false candidates, you are dismissing important new discoveries. You are also robbing time away from any exploration into the unexplored space.
edit: also I think you overestimate the extent to which promising avenues of research are “closed” by a failure to confirm. It is understood that a failure can result from a multitude of causes. Keep in mind also that with a strong effect, you have quadratically better p-value for the same sample size. You are at much less of a risk of dismissing strong results.
The way statistically significant scientific studies are currently used is not like this. The meaning conveyed and the practical effect of official people declaring statistically significant findings is not a simple declaration of the Bayesian evidence implied by the particular statistical test returning less than 0.05. Because of this, I have no qualms with saying that I would prefer lower values than p<0.05 to be used in the place where that standard is currently used. No rejection of Bayesian epistemology is implied.