# Why do polls say that they are accurate + - 3.00% of the time 19/20?

Can you work out the math and say what the real margin of error is. 3 + 0.95%? Would not it be 3.95% to -3.95%. Can one work the math out and explain the margin of error to me?

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## 7 Answers

Maybe it should be + – 3.05%

*Why do polls say that they are accurate + – 3.00% of the time 19/20?*

Context please, I never see the margin of error with “19/20” or other fraction appended.

@zenvelo on Canadian election news they say that the stats are accurate plus or minus 3.5% 19 times out of 20. Also called the margin of error.

So “19 out of 20” is a confidence factor. It isn’t a plus or minus to the margin of error.

They are saying the methodology an the sample size gives them margin of error of +/- 3%, and that 95% of the time the result will fall within that accuracy.

@zenvelo Yes. It doesn’t make sense to me either.

Frequentist statistics is a little counter-intuitive. Let’s say you take a sample and compute the sample mean as some value k. Suppose you assume in this case that the value follows a normal distribution, and to simplify things, let’s assume that somehow you knew the standard deviation.

You look at all the possible normal distributions with the particular standard deviation and mean x. Choose those values of x for which the sample mean k falls with 95% range in an interval centered at x. You could then say that there is a 95% confidence interval for a particular range of x. Suppose x fell between k – d and k+d. You could say that there was a 95% confidence interval value of k +/- d.

if what you were sampling was a percentage value, like percentage of proteins in a person’s diet. Then k and d would be percentage values, so you could say something like, there is a 95% confidence interval that the percentage of proteins is 25% +/- 3%

The important thing to notice is that you are choosing the probability distributions to match the result. Bayesian statisticians don’t care for this approach. They might say that it is like a farmer trying to figure out how a pig escaped from its pen and deciding that the pig must have had wings, because then the chances of escape would be 100%.

A margin of error (ie the chance that the result is not random) of 3% ( 0.03) with 95% confidence tells you that the sample size (n) was 1003 people from the approximation :

Margin of error 0.03 = 0.98 / the square root of n

https://en.wikipedia.org/wiki/Margin_of_error

It’s another way of saying they surveyed 1,000 people.

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