Other Statistical Tests

Several other statistical tests have been developed to provide criteria for rejection or retention of outliers. Such tests, like the Q test, assume that the distribution of the population data is normal, or Gaussian. Unfortunately, this condition cannot be proved or disproved for samples that have considerably fewer than 50 results. Consequently, statistical rules, which are perfectly reliable for normal distributions of data, should be used with extreme caution when applied to samples containing only a few values. J. Mandel, in discussing treatment of small sets of data, writes, “Those who believe that they can discard observations with statistical sanction by using statistical rules for the rejection of outliers are simply deluding themselves.”6 Thus, for small samples, statistical tests for rejection should be used only as aids to common sense.

The blind application of statistical tests to retain or reject a suspect measurement in a small set of data is not likely to be much more fruitful than an arbitrary decision. The application of good judgment based on broad experience with an analytical method is usually a sounder approach. In the end, the only valid reason for rejecting a result from a small set of data is the sure knowledge that a mistake was made in the measurement process. Without this knowledge, a cautious approach to rejection of an outlier is wise.