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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. Return to Common Univariate and Bivariate Applications of the Chi-square Distribution