A comparison of simple statistical methods for estimating analytical uncertainty, taking into account predicted frequency distributions

Error in chemical analysis is propagated mainly by multiplication (not addi tion) of random, systematic and spurious errors. Individual random errors t end to have symmetrical frequency distributions but their combined error di stribution has a positive skew. Certain systematic errors (bias) conceivabl y could have frequency distributions which would enhance or lessen the over all skew but they are unlikely to produce a truly normal distribution. Each analytical method, or modification of it, may produce a unique frequency d istribution of results. Hence an ideal general statistical treatment of res ults cannot exist and the best practical compromise should be utilised. Thr ee simple statistical treatments of data produced from various analytical m odels were compared, to identify the best compromise. Conventional statisti cs, with no transformation of data, generally treated low results too favou rably and high results too harshly. Prior transformation of results to loga rithms tended to do the reverse. Transformation of results to factors, foll owed by derivation of a robust standard deviation, treated the extremes mor e equally, if somewhat harshly. Factor statistics for precision have low se nsitivity to outliers and the assigned true value and they offer a good com promise for the description of analytical data.