Comment author: RichardKennaway 17 September 2014 11:08:21AM *  1 point [-]

It's just my opinion and I honestly don't know a better way to express it right now without being dishonest.

A better way would be to make the criticisms more concrete. What does "not particularly informative and it isn't scientifically sound at all" mean? You might, for example, have said something to the effect that the ellipses are contours of the bivariate normal distribution with the same correlation, and pointed out that not all bivariate distributions are normal. But on the other hand the scatterplots presented aren't so far away from normal that the ellipses are misleading. The ellipses are indeed intuitive and illustrative; but calling them "just fiction" is another way of expressing criticism too vague to respond to. The point masses and frictionless pulleys of school physics problems are also fictions, but none the worse for that.

This is also vague:

Nothing that hasn't been said before, and in my opinion better.

(Where, and what did they say? We cannot know what better resources you know of unless you tell us.)

And this:

I do think it is illustrative, and I do think it has its place. In the newby section maybe.

There is no "newby section" on LessWrong.

Besides, you're talking there about something you previously called "just wrong". First it's "just wrong", then it's "not particularly informative", then it's "illustrative", then "it has its place in the newby section". It reminds me of the old adage about the stages of truth, with the entire sequence here compressed into a single comment.

Comment author: AnneOminous 17 October 2014 09:30:31PM *  0 points [-]

A better way would be to make the criticisms more concrete.

What isn't "concrete" about it? I think the whole article is an exercise in stating the obvious, to those who have had basic education in statistics. Stricter correlations tend to be more linear. A broader spectrum of data points is pretty much by definition "fatter". I don't see how this is actually very instructive. And to be honest, I don't see how I could be much more specific.

Where, and what did they say? We cannot know what better resources you know of unless you tell us.

You mean you've never had a statistics class? Honestly? I'm not trying to be snide, just asking.

Extreme data points are often called "outliers" for a reason. Since (again, almost -- but not quite -- by definition, it depends on circumstances) they do not generally show as strong a correlation, "other factors may weigh more". This is a not a revelation. I don't disagree with it, I'm simply saying it's rather elementary logic.

Which brings us back to the main point I was making: I did not feel this was particularly instructive.

Besides, you're talking there about something you previously called "just wrong".

Wrong in the sense that I don't see any actual demonstrated relationship between his ellipses and the data, except for simple, rather intuitive observation. It's merely an illustrative tool. More specifically:

So this offers an explanation why divergence at the tails is ubiquitous. Providing the sample size is largeish, and the correlation not to tight (the tighter the correlation, the larger the sample size required), one will observe the ellipses with the bulging sides of the distribution (2).

This is an incorrect statement. What he is offering is a way to describe how data at the extreme ends may vary from correlation. Not "why". There is nothing here establishing causation.

If we are to be "less wrong", then we should endeavor to not make confused comments like that.

Comment author: Thrasymachus 02 August 2014 03:01:45AM 4 points [-]

I agree that range restriction is important, and I think a range-restriction story can become basically isomorphic to my post (e.g. "even if something is really strongly correlated, range restricting to the top 1% of this distribution, this correlation is lost in the noise, so it should not surprise us that the biggest X isn't the biggest Y.")

My post might be slightly better for people who tend to visualize things, and I suppose it might have a slight advantage as it might provide an explanation why you are more likely to see this as the number of observations increases, which isn't so obvious when talking about a loss of correlation.

Comment author: AnneOminous 17 September 2014 04:56:53AM -1 points [-]

"At the extremes, other factors may weigh more."

Nothing that hasn't been said before, and in my opinion better.

I don't particularly like your "ellipse" generalization, either, because it's just wrong. We already know a perfect correlation would be linear. We already know a lesser correlation is "fatter". Bringing ellipses into the issue is just an intuitive, illustrative fiction, which I really don't appreciate very much because it's not particularly informative and it isn't scientifically sound at all.

Please don't misunderstand me: I do think it is illustrative, and I do think it has its place. In the newby section maybe.

Understand, I am aware that may come across as overly harsh, but it isn't meant that way. I'm not trying to be impolite. It's just my opinion and I honestly don't know a better way to express it right now without being dishonest.

Comment author: AlanCrowe 05 September 2014 11:07:11PM 11 points [-]

I don't see what to do about gaps in arguments. Gaps aren't random. There are little gaps where the original authors have chosen to use their limited word count on other, more delicate, parts of their argument, confident that charitable readers will be happy to fill the small gaps themselves in the obvious ways. There are big gaps where the authors have gone the other way, tip toeing around the weakest points in their argument. Perhaps they hope no-one else will notice. Perhaps they are in denial. Perhaps there are issues with the clarity of the logical structure that make it easy to whiz by the gap without noticing it.

The third perhaps is especially tricky. If you "re-express your target’s position ... clearly" you remove the obfuscation that concealed the gap. Now what? Leaving the gap in clear view creates a strawman. Attempting to fill it draws a certain amount of attention to it; you certainly fail the ideological Turing test because you are making arguments that you opponents don't make. Worse, big gaps are seldom accidental. They are there because they are hard to fill. Indeed it might be the difficulty of filling the gap that made you join the other side of the debate in the first place. What if your best effort to fill the gap is thin and unconvincing?

Example: Some people oppose the repeal of the prohibition of cannabis because "consumption will increase". When you try to make this argument clear you end up distinguishing between good-use and bad-use. There is the relax-on-a-Friday-night-after-work kind of use which is widely accepted in the case of alcohol and can be termed good-use. There is the behaviour that gets called "pissing your talent away" when it beer-based. That is bad-use.

When you try to bring clarity to the argument you have to replace "consumption will increase" by "bad-use will increase a lot and good-use will increase a little, leading to a net reduction in aggregate welfare." But the original "consumption will increase" was obviously true, while the clearer "bad+++, good+, net--" is less compelling.

The original argument had a gap (just why is an increase in consumption bad?). Writing more clearly exposes the gap. Your target will not say "Thanks for exposing the gap, I wish I'd put it that way.". But it is not an easy gap to fill convincingly. Your target is unlikely to appreciate your efforts on behalf of his case.

Comment author: AnneOminous 17 September 2014 04:27:57AM -1 points [-]

Quote: "The third perhaps is especially tricky. If you "re-express your target’s position ... clearly" you remove the obfuscation that concealed the gap. Now what? Leaving the gap in clear view creates a strawman. Attempting to fill it draws a certain amount of attention to it; you certainly fail the ideological Turing test because you are making arguments that you opponents don't make."

Just no. An argument is an argument. It is complete or not. If there is a gap in the argument, in most cases there are two eventualities: (a) the leap is a true one assuming what others would find obvious, or (b) either an honest error in the argument or an attempt to cover up a flaw in the argument.

If there is a way to "fill in" the argument that is the only way it could be filled in, you are justified in doing so, while pointing out that you are doing so. If either of the (b) cases hold, however, you must still point them out, in order to maintain your own credibility. Especially if you are refuting an argument, the gap should be addressed and not glossed over.

You might treat the (b) situations differently, perhaps politely pointing out that the original author made an error there, or perhaps not-so-politely pointing out that something is amiss. But you still address the issue. If you do not, the onus is now on you, because you have then "adopted" that incomplete or erroneous argument.

For example: your own example argument has a rather huge and glaring hole in it: "bad-use will increase a lot and good-use will increase a little". However, history and modern examples both show this to be false: in the real world, decriminalization has increased bad-use only slightly if at all, and good-use more. (See the paper "The Portugal Experiment" for one good example.)

Was there any problem there with my treatment of this rather gaping "gap" in your argument?

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