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Introduction to Confidence Intervals :: Relationship Between the Confidence Level & Confidence Interval

So as your confidence level increase, your confidence interval gets wider. By the way, there's nothing stopping you from having 96%, 91% or even an 83.5% confidence level. Here's another example.

You ask 12 users to register for a newsletter on a website you're testing for usability. You need to report the average time to the marketing team who's thinking about redesigning the website. After timing 12 users you report an average of 80 seconds with confidence intervals. The figure below shows how the confidence intervals change depending on the confidence level chosen.

So what intervals do you provide to the marketing group? If they want high confidence, you need to use a higher confidence level perhaps 95% or 99%(you need to be more confident of your results). If they just want a ballpark, then use a lower confidence level.

Let's assume they want to be moderately confident. In that case, I think a 90% confidence level will suffice. So here are a few ways you could report the range you observed in your sample of 12 users.

  • The mean time was 80 seconds and we'd expect future samples to fall between 69 seconds and 91 seconds 90% of the time.
  • The mean time was 80 seconds +/- 11 seconds (with 90% Confidence).
  • The mean time was 80 seconds with a 90% confidence interval of 69 seconds to 91 seconds

As you can see, there are a few ways to phrase things. Notice how all three (implicitly or explicitly) contain the confidence interval, the margin of error and the confidence level? All three are critical in assessing statements using confidence intervals.

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