The Art of Statistics: Learning from Data

by David Spiegelhalter

A simple rule of thumb is that, if you are estimating the percentage of people who prefer, say, coffee to tea for breakfast, and you ask a random sample from a population, then your margin of error (in %) is at most plus or minus 100 divided by the square root of the sample size.2 So for a survey of 1,000 people (the industry standard), the margin of error is generally quoted as ± 3%:fn8 if 400 of them said they preferred coffee, and 600 of them said they preferred tea, then you could roughly estimate the underlying percentage of people in the population who prefer coffee as 40 ± 3%, or between 37% and 43%. Of course, this is only accurate if the polling company really did take a random sample, and everyone replied, and they all had an opinion either way and they all told the truth. So although we can calculate margins of error, we must remember that they only hold if our assumptions are roughly correct. But can we rely on these assumptions?

Rule of thumb for margin of error