Parametric Upper Confidence Limit on the Mean

When data are assumed to be normally distributed

The equation used to compute the UCL on the mean when the n data are assumed to be normally distributed is the usual formula (Gilbert 1987, Equation 11.6, page 139): $$UCL = \bar{x}+t_{1-\alpha, n-1}\frac{s}{\sqrt{n}}$$

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),

\(t_{1-\alpha, n-1}\) is the \(100(1-\alpha)\) percentile of the t distribution with n-1 degrees of freedom (Gilbert 1987, Table A2, page 255).

Provided courtesy of ProUCL.

References:

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