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StatsToDo : Sample Size for Estimating Population Standard Deviation

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Introduction Javascript Program R Codes Tables
This page describes the relationship between sample size and error in estimating Standard Deviations (SD) from a sample

As most statistical calculations are based on the critical assumption that the SD of a measurement is known and valid, the precision of an estimated SD is therefore important.

In many cases in the clinical situation, an assumed value for SD is used, based on published figures or from estimates using a small pilot study, but this often results in misleading conclusions

In particular, in engineering and in high precision biochemical laboratories, a valid assumed SD is critical, and the calculations presented in this panel is one of the methods used to obtain this.

The error, the confidence interval of the SD estimated, is expressed as a percent of the value. The greater the sample size, the narrower would be this confidence interval.

Two calculations are offered in this panel

  • At the planning stage of the study, to estimate the sample size required to establish a desired confidence interval.
  • After collecting all the data, to estimate the SD and its confidence interval
The other sub-panels for SD are
  • Javascript program to calculate sample size, and to estimate confidence intervals
  • R codes to do the same
  • Tables of sample size and confidence intervals in the commonly used range of values


Greenwood JA and Sandomire MM (1950) Journal of the American Statistical Association 45 (250) p. 257 - 260

Burnett RW (1975)Accurate estimation of standard deviations for quantitative methods used in clinical chemistry. Clin. Chem. 21 (13) p. 1935-1938