How is it that in the U.S.,surveys of 1,000 are accepted as representative of the entire country?

Question

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?

In: Other

Answer 1

You actually only need 385, if they’re a proper representative sample for a 5% margin of error.

Many people struggle to grasp how statistics works, and are surprised when numbers don’t match their intuition. Like how given 23 random people there’s a 50/50 chance of two people having the same birthday, or 75 random people there’s a 99.9% chance of two people matching. However, if the population isn’t random then different rules apply, like a sampling of a gathering where the people are meeting for a leap-day birthday.

With polling, there is the confidence level and the margin of error that are critical. For a large group like the US, if you ask a representative cross section of people you don’t need tremendous numbers of samples. You can’t ask in a single neighborhood or a single demographic and expect it to represent the nation, but if you’re careful in who you ask it quickly reveals the national trends with relatively few survey samples.

The tighter you want the margin of error the more samples you need. Just 25 people gives a 20% margin of error. 43 people give a 15% margin of error. 97 people gives a 10% margin of error, which is good enough for many surveys. To jump to 5% margin of error you need about 385 people, and a 3% margin of error needs 1068 people. Those are typically what you see in big elections. For very close elections, a 2% margin of error takes 2401 samples, and 1.5% needs 4269 people, 1% needs 9604 people, it’s quite rare for surveys to reach that level.

For elections very often the spread is big enough you only need about 50 or 100 people, more than enough for the trend to be clear. For very close elections a 5% margin might be needed. If they candidates really are at 3% difference, like it has been in a few extremely close national elections, they need a lot of samples to become that much more precise.