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# Understanding margin of error

What is the margin of error in a Mobilityways survey

The margin of error also called the confidence interval and tells you how much you can expect your survey results to reflect the views of the overall population.

You can think of margin of error as a way of measuring how effective your survey is. The smaller the margin of error (<5%), the more confidence you may have in your results. The bigger the margin of error (>5%, the further they can stray from the views of the total population.

The margin of error is a range of values above and below the actual results from a survey. For example, a 60% “yes” response with a margin of error of 5% means that between 55% and 65% of the general population think that the answer is “yes”.

Calculating margin or error  n = sample size • σ = population standard deviation • z = z-score

1. Get the population standard deviation (σ) and sample size (n).

2. Take the square root of your sample size and divide it into your population standard deviation.

3. Multiply the result by the z-score consistent with your desired confidence interval according to the following table:

 Desired confidence level z-score 80% 1.28 85% 1.44 90% 1.65 95% 1.96 99% 2.58

A working example

Assume you are trying to decide between Option A and Option B for a cycle to work scheme within your organisation and your total population (i.e total employees) consists of 1000 individuals.

You decide to survey 300 of those 1000 individuals. This is your sample size.

When you get the results, 60% of respondents say they prefer Option A.  You need to input a confidence level in the margin of error calculator.

This number expresses how certain you are that the sample accurately reflects the attitudes of the total population.

Researchers commonly set it at 90%, 95% or 99%. (Do not confuse confidence level with a confidence interval, which is just a synonym for margin of error.)

Try inputting the numbers from this example in the margin of error calculator above. The calculator gives you a margin of error of 4%.

Remember that 60% of your respondents chose Option A? This margin of error means that now you know with 95% likelihood that 56% to 64% of the total population (your target market) prefer Option A for your new cycle to work scheme.

We arrive at 56 and 64 by adding and subtracting the margin of error from your sample’s response.

#### How sample size affects the margin of error

As we said, knowing your margin of error helps you understand whether the sample size of your survey is appropriate.

If your margin of error looks too big, you will want to increase the size of the sample so that the attitudes of the population surveyed match those of the total population more closely.

What this means is that you will need to send your survey to more people.

The Sample Size Calculator can help you easily determine how many people you need to take your survey.