Improbability Principle

Concerning big numbers. http://m.wisegeek.com/how-many-chemicals-are-there.htm
What can be inferred with this knowledge?

But the chemicals, man!

~~ Paul

The crow study does remind me of the situation with psi. The idea started out based on informal observation guided by confirmation bias and a post hoc ergo propter hoc fallacy. "Published reports" are subject to Chinese whispers when they are chain cited without being read, so the contents of those reports are misrepresented. Then when the idea is tested, based on the kinds of observations which led to the idea, excuses are found to dismiss negative results.

Effect sizes which are visible to the naked eye (i.e. found on informal observation) are likely to be "large", but at a minimum are "medium" (ref. Cohen, Statistical Power Analysis for the Behavioral Sciences, 1988 ed. pg 25-27). So when a "small" effect is ruled out, it rules out the possibility that the informal observations were identifying a valid effect (note that the "% relinquish" measure had a greater than .9 power to detect a small effect). There could still be some other sort of tiny effect there, but it is unlikely to have the characteristics which were assigned to it on informal observation (even if it wasn't in the opposite direction which was initially hypothesized), since those characteristics represented the effects of the aforementioned cognitive biases. Nevertheless, anecdotes will likely continue to win out among proponents of the idea.

Linda

Effect sizes which are visible to the naked eye (i.e. found on informal observation) are likely to be "large", but at a minimum are "medium" (ref. Cohen, Statistical Power Analysis for the Behavioral Sciences, 1988 ed. pg 25-27). So when a "small" effect is ruled out, it rules out the possibility that the informal observations were identifying a valid effect (note that the "% relinquish" measure had a greater than .9 power to detect a small effect).

Of course it doesn't. Anecdotes relate to remarkable behaviour by individuals. A statistical study of the whole population may not be able to detect such behaviour, if it's exhibited by only a minority of individuals.

I agree that when an anecdote is about a remarkable individual, then a different kind of investigation would be more enlightening, like an All or None Case series. In that case, no statistical analysis is necessary because the behavior is outside the bounds of any sort of ordinary range. However, that is not the claim being made in this case. This claim is about a pattern(?) found in behavior crows already engage in.

Should I post links to the original reports?

Linda

I agree that when an anecdote is about a remarkable individual, then a different kind of investigation would be more enlightening, like an All or None Case series. In that case, no statistical analysis is necessary because the behavior is outside the bounds of any sort of ordinary range. However, that is not the claim being made in this case. This claim is about a pattern(?) found in behavior crows already engage in.

Should I post links to the original reports?

Please do, if you have seen reports other than those by Maple and by Grobecker and Pietsch, which concern two crows in total:
https://www.westernfieldornithologists.o...-p0100.pdf
https://sora.unm.edu/sites/default/files...-p0761.pdf

[Laird]

A statistical study of the whole population may not be able to detect such behaviour, if it's exhibited by only a minority of individuals.

True, and it anyway seems to me that one of the fundamental assumptions of the study is at the very least questionable:

If crows use cars to open walnuts, then they should place nuts in the paths of oncoming cars and should not remove them when cars approach. Thus, the frequency of the behaviors Arrive and Drop should be greater during car-present observations than during car-absent observations, and the proportion of departing crows that relinquish their walnuts also should be greater when cars are present.

In the lower-traffic of the two study sites, the average time between cars on a lane was about 90 seconds. That means that at any random time, on average a car will arrive in 45 seconds. That's not long to wait. It seems perfectly plausible to me that a crow with a walnut, not having long to wait on average, would simply drop its walnut and wait, whether a car was visible or not.

In the higher-traffic study site, the average wait for the next car was roughly ten seconds. I'm not even sure how reliable the "car coming" versus "no car coming" observations could be given that level of traffic.

True, and it anyway seems to me that one of the fundamental assumptions of the study is at the very least questionable:


In the lower-traffic of the two study sites, the average time between cars on a lane was about 90 seconds. That means that at any random time, on average a car will arrive within 45 seconds. That's not long to wait. It seems perfectly plausible to me that a crow with a walnut, not having long to wait on average, would simply drop its walnut and wait, whether a car was visible or not.

In the higher-traffic study site, the average wait for the next car was roughly ten seconds. I'm not even sure how reliable the "car coming" versus "no car coming" observations could be given that level of traffic.

Yes - that's essentially what I was thinking of previously when I mentioned the possibility of the crows thinking longer-term. The experimental study was really testing whether the crows were thinking "Here comes something that will crack a nut." But it seems equally plausible that they would be thinking "This is a place where nuts will get cracked." 

In one of the anecdotal reports, it took about 7 minutes for the nut to get run over.

[Laird]

Yes - that's essentially what I was thinking of previously when I mentioned the possibility of the crows thinking longer-term.

Right, I see that now - that'll teach me to reread a thread before posting a "new" insight.

The experimental study was really testing whether the crows were thinking "Here comes something that will crack a nut." But it seems equally plausible that they would be thinking "This is a place where nuts will get cracked."

Yes. Well put.

The author of the first report did not observe a car cracking open a nut. He saw a crow drop a nut in the road and then later return to the road after some cars had driven by. He speculated the rest - that the crow had dropped the nut because cars may crack open the nut, and that the crow returned because one may have done so (although he observed that the walnut appeared to be intact). His speculation that passing cars improve the possibility of a broken walnut turned out to be incorrect based on the study referenced earlier (no walnuts ended up broken by cars in that study over 200 observations). 

The second report was about a crow which twice dropped palm fruits (once it broke and once it didn't) and then returned and flew off with a fragment after a car had run over it and broken it. 

In both cases, the crows were engaging in common crow behavior - dropping nuts on hard surfaces and foraging cracked nuts (the crows also use hard surfaces to strike with their beak at partially cracked nuts, per the study), so it wouldn't be possible to identify whether the crows were remarkable individuals based on those few observations. So one wonders, are there remarkable individual crows and is it possible to identify them? In this case, if there are remarkable individual crows, their number are too small to show up as even a very small effect amongst a group of crows (based on the very high power of the "% relinquish" measure) - that is, true positives are uncommon. Then, given that there will be a high number of false positives - crows which drop and leave walnuts on roads and return to forage cracked or crushed nuts - a "positive" observation is likely to be a false positive, rather than a true positive. So attempting to identify remarkable individual crows post hoc, on the basis of observation, will end up mislabelling ordinary crows.    

I like how this is similar to the questions asked about psi - "remarkable" individuals are identified post hoc using methods which produce false positives (see the OP), and it isn't clear how to distinguish between false and true positives so as to discover whether there is even such a thing as a true positive in the first place.

Linda

[Laird]

Hey, if it's good enough for David Attenborough...