To run experiments on humanity, what's realistic sample size?

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If you're an Eldritch Abomination, Physical God, Dimension Lord, Evilutionary Biologist, Mechanical Monster or Sufficiently Advanced Alien that wants to experiment on humanity, how many of them would make a decent sample selection?

As large a sample size as can be afforded.

Men and women, people of all ages, from all parts of the world.

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That depends on what you want to find out.

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Let's say they want enough to generalize humanity as a species. To categorize us biologically, psychologically, and in controlled societies.

I'd choose randomly 0,5% of each country's population as my sample. Sounds like a good size.

Well you normally don't need that much in total, just like a few thousand from each region.

Depends on your resource allocation. Since the accuracy of a sample only increases as O(n^(1/2)), sampling is highly subject to Diminishing Marginal Returns. Hence why most news reporting only uses a sample size of ~1000-1200 when publishing political polls, etc.

With that said, going beyond 10% of the total population induces bias from non-independence of the sampling population, so that's a definite no-no. I'd say 1000 people from each country is a decent number assuming you have the technology to do so.

Having not done statistics, could you explain this? Surely more views are better, naively?

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I once read a mathematical proof that 1024 is a large enough sample to predict British elections. I can't remember the proof but it looked convincing at the time.

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I recall reading that for a simple yes/no question the magic number is is as low as 30 or so.

Whether you think you can, or you think you can't, you are probably right.

That sounds unlikely, since even sampling everyone can't infallibly give you the result of the election.

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I'm not going to explain math here, but there are results that show that a sample of about a few thousand, as long as it is chosen truly randomly, can give basically accurate results for a population of any size. Of course, this is for individual questions; if you're looking to get a good idea of what humans as a whole are actually like, and the major variations, you'd want to use a stratified sample in those major variations, rather than a simple random sample of the entire globe.

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It depends on how many possible answers there are to the question you are posing, how common each answer is, and what confidence level you are looking for. If some phenomenon is fairly rare you need larger sample sizes to get a meaningful result because you don't want the margin of error to be the same size as the results. For instance, 4% +/- 3% 9 times out of 10 isn't high quality information because your low and high values can vary by a factor of 7 or more.

Whether you think you can, or you think you can't, you are probably right.

@Yej:

In order to do inferential statistics, you need to take a simple random sample of the population. (This means that any particular sample of size N has an equal chance of being selected from the population). You then perform your experiment on the population, and you can infer that these sample statistics will roughly correspond to the population parameters.

The problem is that you need to make sure that the individuals being selected are independent of one another (statistically speaking, that knowing the parameters associated with one individual doesn't affect your blind estimate of what another person's parameters). The problem is that the population is finite. If your sample has a bunch of people whose height varies among the top half of the height distribution, the chance that the next person is also of above-average height goes down. Obviously, with a finite sample, we don't have complete randomness of the sample. However, as long as the sample size is less than 10% of the overall population, the effects of non-independence are negligible.

It's a question of avoiding bias.