I’ve noticed most U.S. polls query around 1,000 people and sometimes even less. Somehow that qualifies for headlines like “Americans say…” or “Most Americans…” How is it acceptable that 0.0002% of the population is accepted as representative?
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Statistician here. It surprises a lot of people to learn that you don’t necessarily need a very large sample to get good information about a group. In fact, assuming an infinitely-sized population, it’s possible to get meaningful results with a sample as small as 385!
At it’s core, statistics is about getting information about a large group (the population) by examining a smaller group (the sample). It’s assumed that the sample is an accurate reflection of the population. This is likely to be true because of probability. At a certain point, it’s mathematically improbable for the sample to be too different from the population.
Let’s say that you have a jar full of 500 green marbles and 500 orange marbles (50% of each). You randomly pull out 100 marbles. Mathematically, you’re probably going to end up with 50 green marbles and 50 orange marbles, or at least pretty close to that. It may be technically possible to get lucky and pull out 100 green marbles, but that’s so unlikely that it’s not much of a concern. Sampling is the same way. At a certain point, it’s extremely unlikely that the sample will be radically different from the population.
There is a catch here–the sample has to be taken randomly. If I were to look for green marbles to pull out of the jar, it’s not going to accurately represent the jar’s contents. Likewise, samples need to selected randomly from the population to be valid. In practice, this is almost never the case, especially for large samples. You will always have a sampling method that excludes people or a number of people who don’t respond after they’re selected. However, surveys still have to assume that the sampling was random. That’s why it’s important to look at the sampling method used by the poll, and pay attention to multiple polls to make up for the errors in individual surveys.
If it helps, here’s a [sample size calculator](https://www.calculator.net/sample-size-calculator.html) that you can use to look at how big the sample needs to be for a survey. As stated earlier, using an infinite population, a confidence level of 95%, and a margin of error of 5%, you would only need a sample of 385. That’s on the higher end of acceptability though, but you can play around with other numbers to find out a better sample size.
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