This is a nice example showing how a little empiricism can really help you sort through some sticky statistical issues.

“True, but how many times does a social scientist work in a situation where the variance is not moderate?”

For example: suppose you’re asking your study participants how many sexual partners they have had. (For this discussion, I will leave aside the obvious problem that they may not respond truthfully). Most of the sampled population will give a low numbered response, but a few are sex industry workers who will give a very high response. To get an accurate estimate of the mean, you need quite a large sample.

But yes, in many situations the underlying distribution doesn’t have a very long tail, we’re not dealing with rare events, and a sample of 50 or so is quite adequate.

Funny, a few people hold the opposite opinion.

the study was based on “investigators” going out and taking notes on parent/child interactions in supermarkets (and rating their attractiveness while they were at it). It seems to me that these kinds of “studies”—and the college student one you describe—are DESIGNED not with the serious research paper but with the titillating press release in mind.

I don’t work in psychology nor sociology, but I simply cannot believe there exists an entire discipline in which this kind of thing is taken seriously (evolutionary psychology is more an ideological disposition than a discipline, so that doesn’t count as a counter-example).

True, but how many times does a social scientist work in a situation where the variance is not moderate? For example, if we wanted to study voting, how badly would the CLT be violated? Furthermore, as Walt said, it’s not a problem if you have truly random sampling.

My perspective on a lot statistical issues is that social scientists often analyze data that behave fairly well, even though they don’t perfectly satisfy the assumptions of many models. The goal is not accuracy (which is an issue in engineering) but measuring general tendencies among variables. E.g., we don’t care exactly how much income increases with education, but we’re happy as long as we get a reasonable ball park figure. Most samples of modest size are good enough to answer this type of question.

The problem Ester Hargatti identified has to do with an extreme violation of randoming sampling principles. No amount of statistical technique will help you if your sample is massively biased, say, by selecting only 18-22 year-old college students.

Bob McManus said:”“You don’t need huge samples to draw valid inferences.”

Well, I did work quality control for a while, and do understand a little about sampling. Very little. But human beings are not widgets.”

I never claimed people were widgets, but the amazing thing about a well constructed sample is that you can obtain pretty good answers with very little data. It’s an amazing statistical fact that a small random sample can tell you a lot about a huge population.

Furthermore, it’s not the relative size of the sample – it’s the raw size of the sample. In other words, a random sample of 1,000 tells you the same about a ten thousand or a million people. It’s hard to believe, but it’s true. It blew my mind when I first understood this.

Engineer: “That’s really cool – all the sheep in Wales are black”

Physicist: “But you’ve only seen one! The best you can conclude is that at that there is at least one black sheep in Wales.”

Mathematician: “You’re both wrong. At least one sheep in Wales is black on at least one side.”

Well, he posts on three blogs – his own, TAPPED, and at TPM Cafe.

And possibly others I am not aware of.

That is beautiful – i am putting that on my door at work.

The assumption that the central limit is Gaussian, or approached in any reasonable amount of time only applies when the distribution has moderate variance. Information systems (like human minds and the internet) can routinely and easily produce non-Gaussian central limits because, IIRC, among other things, they have memory and ordered behavior, and are also capable of communication. Which doesn’t mean the Gaussian distribution is wrong in all such cases, but does mean that it is unreasonable to assume it. See Mandelbrot, passim.

2. Was the woman providing encouragement? Please bear with me, I don’t mean in some obvious crass way. Previous experiments have show (see The Person and the Situation, by Ross & Nisbett) that a man talking to a woman he cannot see but believes is attractive will speak to her differently than he would were he to believe she is not attractive. Furthermore, and this is the important point – observers listening only to her end of the conversation rated her response as more engaging when the man believed she was attractive. There is unconcious feedback.

Overall this study seems to flawed—they are looking for dispositional factors to explain bad behavior when situational factors are far more important. They would do far better to study the environments in which harrassment has occurred and try to find common elements there.

ps. It kills me whenever someone 40+ yaps about women vs. men. Gender roles have changed dramaticly in the past 40 years and continue to do so. There is no state of nature we can make our measurements with respect to. Behavior on the part of women that would once have been considered pathological is now relatively normal. We may have started as chimps but we may end up as bonobos.

The problem is that the researchers cannot evaluate their assumption that all people everywehere work the same, because they just do not have data that data to do that evaluation, i.e. they have only data from college first years, or people under treatment at major research hospitals.