What is the difference between margin of error and confidence interval?

Answer 1

From what I can understand, the difference is a technical one: the average person might equate one with the other.

A confidence interval is defined to be an interval where you are x% sure that your true value lies.

So if I estimated your weight was... 250 lbs (~113 kg or ~18 stone) but said that my confidence interval was 99% for the range of 50 lbs - 500 lbs, that could be true (but worthless).

You can see how problems could arise: the larger the interval (range of values), the higher confidence I can have that the true answer is somewhere in there.

But the larger my range of values, the less accurate it is as a whole - as in my earlier example, if I estimated your weight to be between 50 - 500 lbs, it would be technically correct, but useless if we were trying to figure out how many people we were trying to fit on say, the last helicopter out of Saigon.

A margin of error, statistically speaking, (MoE) is simply defined (as far as I can tell) as a confidence interval of 95%.

Notes:

A margin of error shrinks as the sample size grows. A good way of estimating a margin of error is the expression (0.98)/(sqrt(n)), where n is the size of the sample in question.

You may note that many polls in the news have a margin of error of 3.1% - this is due to the fact that many polls use 1,000 people for a nice 'round' number.

A margin of error is unavoidable and ONLY REFLECTS THE SIZE OF THE SAMPLE.

It does not, I repeat, not indicate any mistakes in the way the survey is carried out. A sample of 2,000,000 Adolf Hitlers would have a MoE of only 0.06% but might indicate that the continent of Europe believes in the therapeutic power of racial cleansing.

Final note:

Different people may use the term 'margin of error' slightly differently. Clarify, clarify, clarify!