> ... but know a P value of < .05 (in this case, 39/47 is more like .000001) is pretty strong evidence of the conclusion.

This is false, and the fact that it's false has been proven and accepted for years.

http://www.nature.com/news/scientific-method-statistical-err...

Quote: "P values, the 'gold standard' of statistical validity, are not as reliable as many scientists assume."

http://bigthink.com/neurobonkers/the-statistical-significanc...

Quote: "P<0.05 is the figure you will often find printed on an academic paper, that is commonly (mis)understood as indicating that the findings have a one in twenty chance of being incorrect."

Also, your effort to estimate the probability of 39/47 is seriously flawed -- it depends on the distribution of successes and failures within the list.

> At what point do you say "The hypothesis that a professional investor with a published strategy who returns the best-performing fund in history appears to not be based on chance?".

Have you been reading my replies? The answer is never. The scientists at the LHC have acquired a p-value of 5-sigma for their observation of the Higgs, meaning the probability that their apparent detection of the Higgs arose from chance is 2.8 * 10^-7 (the "p-value"), but guess what? They are never going to say, "We detected the Higgs." Only ignorant science journalists say things like that, in the same way that ignorant stock market journalists say, "So-and-so has a reliable method for beating the market."

> Do you really think beating the market long-term is a simple 1-time standard deviation computation?

Yes, that's exactly what it is, given adequate data. And if that cannot be done, then economics has earned its reputation as a non-science.

> Do you really think 2% of investors (1 in 50!) achieve 20% compound growth over 48 years?

That was a hypothetical example, don't try to use it as an argument.

> I thought it was impossible, now 50% of people will consistently beat the market long term by any margin?

You will need to try to edit your posts to make them comprehensible. If you're asserting this viewpoint, I can prove that, for a random market with random buys and sells, with millions of investors, (a) 50% will do better than the average (uncontroversial), and (b) many of them will become rich by chance alone -- not just do better than the average, but become very rich with a small initial stake. Details here:

http://arachnoid.com/equities_myths/index.html#Market_Model

> Per the cited article, from trained economists ...

What? You're invoking the authority of "trained economists" to bolster your viewpoint? First, economists aren't scientists, second, an appeal to authority is a logical error, and third, your choice of quotation supports my view, not yours.

But I ask you to examine your position, and I shall help you do this by way of a reductio ad absurdum. Let's say there's a system for improving on average market returns, that it's something other than a chance outcome, and that it can be defined, tested, and thereby proven to exist in a scientific sense -- that it can be raised above the level of cocktail chatter.

1: Thesis: There is a way to trade securities that can be assured to reliably improve on average market returns, by means other than chance. The method can be written down, and therefore it can be tested objectively.

2: If (1) is correct, then anyone could take the proven, defined method, apply it to the market on a large scale, and drain it of all its capital in a short time.

3: But, notwithstanding the certainty of human greed and simple curiosity, (2) has not happened, anywhere, ever.

4: Therefore (1) is false.

Why is that definitive? Because science cannot be just descriptions ("Warren Buffett has an equities track record"), it requires explanations ("This is why Warren Buffett has an equities track record"). If there is no explanation, there's no science, and there's no point in conversations like this one.

Anyone can describe something in the environment, but the only interesting ideas are those accompanies by a testable explanation, a theory that purports to explain some aspect of nature, a theory subject to empirical test. And the outcome is interesting whether the theory turns out to be true or false -- we learn just as much from false scientific theories as true scientific theories.

And this is a classic debate between someone who understands science, and someone who doesn't.