Tip: calculating margin of error of a %

It’s handy to be able to calculate a margin of error, and you can do it in 10 seconds on your calculator.  (You’ll need a calculator with the square root button on it).

 

The formula for calculating the margin of error of a percent at the 95% confidence level is: the square root of ((P * 1-P)/base) * 1.96  (where P is the percentage for which you want to calculate the margin of error )

 

Example: an answer of 65%, with a base (sample) size of 150. What’s the margin or error?    

  • .65 * .35 = .2275
  • .2275/150 = .00152
  • square root of .00152 = .0389
  • .0389 *1.96 = .076

Now convert .076 back to a percent = 7.6%, and that’s the margin of error.

 

And, to put that in English, if we surveyed everybody (a census) we’re 95% sure that they would answer between 57.4% (65% - 7.6%) and 72.6% (65 + 7.6%).

 

Tip you may hear people saying things like “the margin or error for a sample of 1,000 is plus or minus 3%”.  But you can see from the above that the margin or error depends not just on the sample size but also the answer (the percent) and the confidence level. The reason is that when we talk about margins of error at different sample sizes, we’re assuming a percent of 50% (which is in fact the value at which the margin or error is highest) and a confidence level of 95%.