This Margin of Error calculator lets you see how confident you can be about survey results given four factors:
(b) the confidence level you wish to have (90%, 95% or 99%),
(c) the population being tested, and
(d) the proportion being tested (usually 50%, the “worst case”).
The margin of error (also called the “confidence interval”) is expressed as a range in terms of percentage points. As an example, if you were to survey 300 people and wanted a 95% confidence level, assuming the population being studied was more than 30,000 individuals, the margin of error for the total results would be +/- 5.66 points. If one result was that 55% of the sample said they knew of one thing, and 40% said they knew of another thing, the difference of 15 points would be statistically significant at the 95% confidence level since the 55% result would have a margin of error between 49.3% and 60.2%, and the 40% result would have a margin of error between 34.3% and 45.7%.
“Confidence level” is expressed as a percentage and refers to the degree of confidence. One way to think of it is that if you were to hypothetically run the test (survey) 100 times with similar respondents at the 95% confidence level, 95 out of those 100 times you would obtain the same results within the confidence interval. For social science market research, 95% confidence level is sufficient.
As noted in the calculator, you do not need to enter the population size being tested unless your sample will be over 1% of that population, in which case the margin of error calculation will improve depending on the population size. So, if you were planning to survey 50 CFOs of the Fortune 500 companies (10%), your margin of error will be +/- 13.16 points at the 95% confidence level, slightly better than a survey of 50 CFOs of the top 10,000 companies (0.5%), where the margin of error will be +/- 13.86 points at the 95% confidence level.