STATISTICAL TECHNIQUES FOR COLLABORATIVE TESTS FOREWORD This manual presents statistical techniques that may be used in collaborative testing of analytical methods. It is an introductory guide issued for use by the AOAC's Associate Referees, whose statistical backgrounds cover a wide range. Every effort has been made to keep the presentation simple and flexible, and to hold the statistics to a minimum. Special attention is focused on planning the collaborative test and presenting and interpreting the analytical results. Obviously the laboratory proposing a new method should study the method carefully before a collaborative trial is undertaken. Section VI D of this handbook gives an efficient program for a within-laboratory examination of a method. An important innovation is that materials be chosen in pairs (Section V). The two members of a pair should be similar in nature and amount present. Such a pair becomes a "unit block" in the collaborative tests. The concept of the unit block leads to an easy statistical analysis and graphical examination of the data. The data from several unit blocks are readily presented in summary form. The concept of the unit block allows a way to utilize the services of smaller laboratories not having the resources to participate in some of the more comprehensive collaborative studies by having them participate on only the unit blocks of materials in the range of interest to them. It is not necessary that each unit block have the same number of collaborators. As a guiding rule, as many collaborators as possible should be obtained-up to 30 collaborators per unit block. At the minimum level it is suggested as a guide (not as a standard) that the number of collaborators be maintained at not less than six, if possible. We must recognize that situations sometimes exist which severely limit the number of collaborators that can be obtained. This rule is certainly not intended to cut off such investigations because an arbitrary minimum number of collaborators cannot be found. I firmly believe that any data properly taken are better than no data. To properly interpret the analytical results of a collaborative test, the scientist must give careful consideration to the various sources of error in the data obtained. Any analytical result is a complex of three factors: (1) the random error; (2) the inherent systematic error in the procedure; and (3) the modification in this systematic error that is a consequence of any particular laboratory's environment, equipment, and any personal way of using the procedure. One modern trend is the increasing use of reference materials and the adjustment of instruments to make them deliver the known values for the reference materials. Properly used, the reference materials delete the second and third factors mentioned in the preceding paragraph. There is a disadvantage, however, because the process of adjusting the instrument also involves a random error. The standardization of a volumetric reagent is a similar situation. There is still the random titration error in determining the titer. But this random error, which now becomes a part of the titer value, acts as a constant, or systematic error, when the reagent is used on a series of unknowns: Any error in the value of the titer is directly carried over into every result. Consequently at least three or four titrations should be made when standardizing a reagent. The average of these repeats allows a certain degree of cancelling out of the random errors. The random error in the average of four is just half that of a single titration. This reduces the random error in the titer value to the point at which, now acting as a systematic error, it is smaller than the random error of a single titration on an unknown. This averaging device is not possible in the adjustment of instruments. Most introductory statistical texts are necessarily limited to the consideration of very simple experimental situations. After all, the statistical student has to begin his learning with simple techniques. The real world of measurement is usually an intricate place and requires careful examination by the scientist to enumerate the various sources of error in his measurement. Since a statistician without much experience may easily overlook the hidden complexities in an unfamiliar field of measurement, the scientist must not shirk the responsibility for the interpretation of his data. This is the best reason for writing this manual, which represents the initial action in filling a recognized need for statistical guidelines in analytical method studies. Comments and suggestions from the users are invited. Further developments along these lines are intended, and revisions, additions, and deletions will be made as experience dictates. Published by the Association of Official Analytical |