Clarifying Statistical Usability
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Step 3 of 9: Standard Deviation
Be warned: If you have no background in statistics the next few steps are going to seem a little like voodoo. But while the concepts may seem a little obscure, the good news is that the calculations are all pretty straight forward.
In order to finish calculating our Confidence Interval, we need to calculate the Standard Deviation. We get to the Standard Deviation by first calculating the Variance. Both Standard Deviation and Variance are a measure of the spread of the sample data.
It makes more sense if you think about a time-on-task example. In the two graphics above, the average time-on-task is the same. But in the first example (short spread) the individual participants' time-on-task are all very similar. There are just a few seconds differentiating the shortest time from the longest time. In the second example (wide spread) the individual participants' time-on-task are very different. One participant may have taken just a few seconds to accomplish the task while another participant perhaps took 10 minutes.
To calculate the Variance (and then the Standard Deviation), we refer to our observed Completion Rate:
| Calculated Data | Symbol | Formula | Value |
|---|---|---|---|
| Variance | s2 | p (1-p) | .9(1-.9)=.09 |
| Standard Deviation | s | SQRT(s2) | SQRT(.09) = 0.3 |