A standard scheme for calculating numerically standard deviations and confidence intervals

A quick and universally applicable standard scheme is outlined for the calculation of standard deviations based on the general equation for error propagation: With this method, standard deviations are calculated numerically without violating the condition of mutually independency, with substantial time gain and with no risk of calculating errors. The Welch—Satterthwaiteʹs approximation of the degrees of freedom is a logical extension of the technique with which confidence intervals can be easily established. Direct insight is obtained about the separate contributions of the different error sources and the influence of correlation. Practical examples are given to demonstrate its usefulness in case of comparison of (dependent) results after a regression, calibration lines with separate pretreatment and correlation.