Studies on computer-simulated models have provided several new methods of estimating, studying or controlling analytical precision in real systems. The methods are based upon precision estimators derived from the difference between duplicate analyses, and take into account variations in the precision of a determination with the concentration of the substance being determined. The methods have been checked by applying them to simulated samples of many duplicate analyses drawn by Monte Carlo techniques from specified populations, that is, in effect, from analytical systems with known precision characteristics. Some examples show the application of the methods in practice.