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
If you’re curious about the actual math used, margin of error calculations typically depend on the Central Limit Theorem. This is a theorem that says if you take a sample from the population, the amount that your result will deviate from the true value follows a Normal distribution. The Normal distribution is a well-understood probability distribution, so you can assign a probability to any amount of deviation. The margin of error is usually selected to ensure that there is a 95% chance the true value is within the range defined by the margin of error.
The Central Limit Theorem also says that the sample size affects the resulting error distribution. The more people you survey, the tighter the distribution, so the smaller the margin of error.
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