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Introduction to Confidence Intervals :: Variability Affects the Confidence Interval

So you may be asking yourself, so what, one population has a lot more variability that the other, but why does that affect the width of the confidence interval?

Well lets say you had to report the average time for both versions but didn't have the time to test the whole population of 20 users (since that's usually the scenario--you have to sample a small portion of a larger population). Instead you only had time to test 4 users (2 for each website version) and then provide your best guess of the average times.




Version 2 with its higher variability would have values that would wander further from the average of 60 seconds that we know the whole population takes. Now, normally you almost never know what the total population average is ahead of time, but for this example we do so we can see why a more variable population creates wider confidence intervals.

Here are those times again:

Version 1
Avg. Time: 60 Seconds (10 Users)
Version 2
Avg. Time: 60 Seconds
(10 Users)
  95
48
71
50
74
40
25
64
51
82
150
21
100
40
33
74
12
133
21
16

 

Try it for yourself, watch how the 2 user sample from Version 2 wanders further from 60 seconds. The calculator below picks two random people's task time from each population of 10 users from above and generates their average time.

Click the button many times and compare the average times.

 
  Average Average

Did you notice how the sample from Version 2 had average times that were wandering further from 60 seconds than the sample from Version 1?

If we needed to be 95% sure that the next sample would contain the mean, you can see that with more variability, we're going to need to cast a wider net--in other words, have wider confidence intervals to get a better picture of where the mean is.

We were picking only 2 out of 10, but this is the same principle that applies when you're picking 10 from 1,000 or 1000 from 280 million. The variability of the sample will affect our best guess at the true value of the mean and so our confidence intervals will reflect this.

We'll get into the mechanics of calculating the variability using something called the standard deviation next. For now, remember than with more variability comes wider confidence intervals.


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