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What are confidence limits and intervals?

After having a number of clients ask what confidence limits actually means we decided it was about time we shared the explanation more widely.

As a novel start-up in a poorly-researched space, we needed to validate the problems Whirli is solving. Sapio Research were fantastic partners from start to finish – creative in brainstorming angles, careful in designing the questions, and rigorous in analysing the results. The research brought a wealth of insights, backed by hard figures, for our business decision making and for us to talk about publicly in the press.

Nigel Phan

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After running an online consumer survey with Sapio or another market research agency, you may have noticed statistical terms like “confidence limits” or “confidence intervals” being mentioned in the research methodology, similar to the phrase shown below:

“Results are accurate to ± 3.1% at 95% confidence limits assuming a result of 50%.”

After having a number of clients ask what this classic line actually means we decided it was about time we shared the explanation more widely.

In a nutshell: Confidence Intervals are a way of measuring how well your sample represents the population you are studying.

For example, imagine you’ve run some research with 1000 consumers; a key finding is that 50% of your sample agree that 5G causes COVID-19. (Quite a worrying stat which I think you’d be quite right to question the accuracy of!)

How do we know how well this represents the total population of consumers as a whole?

This is where confidence intervals and margin of errors come into play:

  • The Margin of error tells you how many percentage points your results could differ from the real population
  • The 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.

So, what does the sentence actually mean in context of our 5G example?

If you have 50% of the sample agreeing that 5G causes COVID-19 –  then you can be 95% confident that in the real world 50%, plus or minus 3.1%, (i.e. between 46.9% and 53.1%) of consumers actually agree with this.

The more extreme the percentage of interest is, the smaller the margin of error gets. (i.e. the further away from 50%, the smaller the margin or error)

How can you increase the likelihood of accurately representing the population in your research?

Increase your sample size!

As a sample size increases, the range of interval values will narrow. This makes the mean value more accurate compared to with a smaller sample.

You can use the diagrams below to work out the sample size you need to achieve a certain margin of error:

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