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%.