Confidence interval of a SD



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 . You simply enter the sample standard deviation and sample size and click “Calculate now.”

[pic]

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

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download