How to calculate the margin of error

This calculator calculates the error associated with the sampling approach, also known as the "sampling error". See this article for an explanation of the types of error which impact the accuracy of market research: Understanding errors in research

Sample Size: the number of respondents to your survey

Population:the number of people that your sample is meant to be representing. I.e. if you could ask everyone relevant (e.g. the population of the UK)

At which percentage: Defaults to 50% if you don't enter anything. The error changes depending on on what percentage you report it at; as the errors are assumed to be normally distributed, the error will be maximum when your result (percentage of the sample) is at 50%.

The calculation gives the error which is significant at a 95% confidence level.

The percentage margin of error is ± %

Types of errors in survey research

Sampling Error: The error most frequently quoted alongside a result from a research survey is the Sampling Error. All this can tell us is the probability that the value reported will be within the given range if a HOST of different assumptions about the sample compared to the population are met, as well as the survey design.

Nonsampling errors:Things like nonresponse error and measurement error. The issue with these other types of error is that they are much harder to quantify:

Errors related to sample design

Coverage Error: Did you reach all the types of people that your sample is trying to represent (undercoverage)? Did you ask some people who weren't in the target population (overcoverage)? i.e. is your sample representative of the population you're researching. Coverage error results from selection bias, and is likely to be bigger for some sample designs- convenience sampling for example. It's pretty much impossible to know how large this is. We can compare against census data to see if your demographic profile is about right, but can't compare with regard to survey mode (who answers their phone vs. takes surveys online) and those who are generally hard to reach.

Nonresponse Error: How do we know what the people you didn't ask were going to say? Similarly difficult to measure as you need to know who didn't answer your survey. See my article on weighting for more on this.

Errors related to survey/questionnaire design

Measurement Error: This is generally about people giving answers that don't accurately reflect the truth (be it deliberately or not). This can be due to cognitive biases, or social norms and pressures, but it can also be due to bad survey design, due to things like framing and anchoring. Measurement error can be looked at through the lense of Validity and Reliability

Validity is about how well a value derived from a survey correlates with the true value.

Reliability is about how much a response varies when you take the measurement repeatedly. Nice way to think of it below: