## Learning about Margin of Error

When dealing with percentages/sample or population proportions, a quick and the most conservative margin of error you can create for any of the percentages or proportions, without having to figure in each specific percentage/proportion you want to look at, is the maximum margin of error. You just need the sample or population size, and you get a one-size fits all conservative margin of error, the maximum margin of error. I’m no expert on this of course, as a disclaimer, so don’t let me lead you astray if I’m wrong about any of this.

From Wikipedia:

### “Maximum margin of error

The maximum margin of error for any percentage is the radius of the confidence interval when p = 50%. As such, it can be calculated directly from the number of poll respondents. For 95% confidence, assuming a simple random sample from a large population:

(Maximum) margin of error (95%) = 1.96 × $\sqrt{\frac{0.5(1-0.5)}{n}} = \frac{0.98}{\sqrt{n}}$

This calculation gives a margin of error of 3% for the Newsweek poll, which reported a margin of error of 4%. The difference was probably due to weighting or complex features of the sampling design that required alternative calculations for the standard error. It is also possible that Newsweek have rounded conservatively to avoid overstating the confidence of their results.” (see the full Wikipedia entry for context re: the Newsweek example.)

More on margin of error from Wikipedia:

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.

Here’s a neat chart of maximum margins of error, via research company Synovate. You could quickly throw something like this together in Excel.

 Sample Size At 95% confidence At 90% confidence 60 100 200 300 400 500 600 700 800 900 1000 +12.7% +9.8% +6.9% +5.7% +4.9% +4.4% +4.0% +3.7% +3.5% +3.3% +3.1% +10.6% +8.2% +5.8% +4.7% +4.1% +3.7% +3.3% +3.1% +2.9% +2.7% +2.6%