# Constructing a Confidence Interval for the Standard Deviation

```Construct a Confidence Interval for the Standard Deviation
Although I always teach my graduate students how to construct (with 2) a
confidence interval for the variance, I have never, until today (the 7th of November,
2010) actually needed to do so for research purposes. A doctoral student in Education
needed to test the null hypothesis that the population variance in a variable is zero.
Rather than go the usual route of computing 2) and obtaining a p from that test statistic
(which I would need to by hand), I took the easy approach and found a web app that
would construct the confidence interval for me. Since the student had reported the
standard deviation rather than the variance, I used an app that calculates the CI for the
standard deviation. The app is at http://www.graphpad.com/quickcalcs/CISD1.cfm .
You simply enter the sample standard deviation and sample size and click “Calculate
now.”
Confidence interval of a SD
Parameter
Value
SD
0.8374800
SEM
0.1341041
N
39
90% CI of the SD
0.7065819 to 1.0349190
95% CI of the SD
0.6844291 to 1.0793275
99% CI of the SD
0.6444107 to 1.1754711
These results assume that you have randomly sampled data from a population that is
distributed according to a Gaussian distribution. Note that the confidence intervals are not
symmetric around the SD. This makes sense. SD values must be greater than zero, so the
uncertainty for the upper confidence limit extends further than the lower limit.