Google says that the margin of error is “The margin of error is a statistic expressing the amount of random sampling error in a survey’s results. The larger the margin of error, the less confidence one should have that the poll’s reported results are close to the “true” figures; that is, the figures for the whole population.”
But how do they know how wrong they are? Is it just bullshit?
In: Mathematics
A margin of error is a rigorously determined statistical calculation – there are precise formulas for it. It’s not a general statement of “how wrong could we be.” It really more of an assessment of how much your sample size may not be a good representation of the entire population you wish to sample.
If you want to know the preference between vanilla or chocolate of everyone in a town of 100,000 people, you could ask each of them and report what you find. Your finding would have no margin of error – you asked everyone and reported the percentages based on that. The point of a poll is that you don’t want to ask everyone, you want to take a much smaller sample and use that sample to extrapolate results for the entire population. The smaller your sample size, the greater the margin of error.
If you sampled 80,000 people (randomly, controlling for bias), you’d be pretty darn sure you’ll get very similar results as your total-population survey. If you asked 2 people, you’d have very little confidence that your results track the entire population. You can determine exactly how confident you should be that your sample results reflect the entire population, and that is expressed as a “margin of error.”
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