VSP uses the following approximate Chebyshev formula to compute the UCL when no assumption is made about the distribution of the data:
$$ UCL = \bar x + \sqrt{ \frac{1}{\alpha} -1} \frac{s}{ \sqrt{n}} $$
Where:
\( \bar x \) is the sample mean, \( s \) is the sample standard deviation and \( n \) is the number of data points (see the Summary Data Sub-page for these values),
\( \alpha \) is a value between zero and 0.5 such that a 100(1- \( \alpha \)) percent upper confidence interval is obtained . For example, a 95 percent UCL is obtained if \( \alpha \) is set equal to 0.05. The rationale for using the above Chebyshev UCL formula is provided in ProUCL (2004, page A-32).
Conover, W.J. 1999. Practical Nonparametric Statistics, 3rd edition, Wiley, NY.
Gilbert, R.O. 1987. Statistical Methods for Environmental Pollution Monitoring, Wiley, NY.
ProUCL. 2004. ProUCL Version 3.0 User Guide April 2004. Available for download from http://www.epa.gov/nerlesd1/tsc/tsc.htm