Hacker News Reader

Are you questioning random samples? Seriously? The notion of representativeness is flawed and often does not work well in practice, i.e. it often leads to biased estimates. Unless there is a good reason for not doing a random sample (mostly for economic considerations), simple random samples are fine.

I'm not questioning random sampling. Quite the opposite, and I even said as much in the comment you responded to:

> There is a good reason to do a random sample rather than try to construct a representative sample, but the article just brushes past it!

It's a simple starter example in a blog post. Stratified sampling, with pros and cons, is covered in an intro stats course. This is not an intro stats course, it's a short article on a blog.

>Any statistician worth their salt can see the problem with an operational definition of height that starts with "bottom of their feet".

I don't get it, what's the problem with that?

When field workers go out to measure people from their feet they will inevitably encounter someone who does not have feet. The ambiguity of how the definition applies to this case can easily lead to field workers doing weird things like substituting (non-randomly) people with feet for those without, or trying to guess "if this person had feet" or simply omitting that unit from the sample entirely.

Either one of those methods are fine, but leaving it unspecified is a threat to external validity.

I thought the catch was going to be people who cannot stand upright.

In theory you could have rigourous guidelines that span pages and cover as many edge cases as possible. That's besides the point of the article. Finding an edge case in a definition mentioned in passing doesn't really give you a lot of ground to criticise the statistical approach. It's just nitpicking which distracts from the overall point.

> > For a simple starter example, we know that every person on Earth has a height, defined as the distance from the bottom of their feet to the top of their head when standing upright.

> This is a silly mistake to make in an article on statistics. Any statistician worth their salt can see the problem with an operational definition of height that starts with "bottom of their feet".

You missed the forest for the trees.

> Why would we select a subset at random? Why shouldn't we try to select a representative subset? We know from experience that biological sex, country of birth, and affluence of family are three strong predictors of height. Why shouldn't we deliberately select a subset that balances out these variables in proportion to their population?

Random subsets are core to statistics, and they are independent of representative samples. You choose random subsets so that you can compute statistics with well defined confidence intervals (as in the less randomness there is in your sample the poorer/hard to quantify your confidence would be).

You use representative samples when you want to compare groups. Representative samples should still be random per group.

>Why would we select a subset at random? Why shouldn't we try to select a representative subset?

Isn't this similar to the point this article is trying to make? Looking at statistics as a collection of algorithmic recipes shifts attention to how those procedures are designed, and when do they yield us useful summaries. When you want a "representative mean" rather than the population average, you'd just tweak your algorithm.

The mean from a representative sample is, if you got the representation right, "equal" to the mean from a random sample, and both are "equal" to the population average.

The problem with representative samples is that you can't know whether you've actually constructed one, and even if you have, you'll find it hard to compute the errors of your estimations.

My beef is not with thinking of traditional frequentist-objectivist statistics as a set of algorithms solving specific problems (because that's what it is), my beef is with not starting out explaining exactly when the algorithms apply and why.

When you take a black boxy algorithmic approach to something, you have to be particularly clear about things like that.

> We know from experience that biological sex, country of birth, and affluence of family are three strong predictors of height.

I guess that an even better predictor is the parents' height.

In some countries/eras the next generation is reliably much taller than the parents as non genetic factors dominate.

I'm not sure how the numbers play out but would expect that to be a big confounding factor given changes in global poverty.