Papers - Sampling and Analysis - Statistical Interpretation of Laboratory Coal Tests and Sampling Methods (T. P. 849, with discussion)

Every mathematical statement of a measure of anything (as distinguished from a count') is followed by a qualification—always implied if not explicity stated—-that the statement is only an estimate, which may vary from absolute accuracy within certain limits, according to the accuracy of the measuring instrument. This basic fact, so obvious to engineers, is not so well understood by many that make use of laboratory coal tests. The tolerances that must be allowed in measurements of coal quality are very important in both their commercial and engineering applications—and the significance of these tolerances depends upon the use made of the laboratory coal test. Only in recent years has there been any intensive study of this question of tolerances as applied to measurements of coal quality. There is very little in our published literature on the subject, and what has been published is not readily comprehended by those who sell coal, or buy coal and use it, unless they happen to have made a study of the subject themselves. There is great need for more widespread understanding of what lias been discovered and how it applies to the use of laboratory coal tests. What follows is an attempt to condense into a few pages the results of the major investigations so far reported, and to explain their meaning in simple nontechnical language, with the addition of some recent illustrative experiments. Determining Deviations in Quality It is necessary at the outset to distinguish between: (I) the accuracy with which one test indicates the quality on one lot of coal; and (2) the accuracy with which a test of one lot of coal represents the average quality of a commercial product, of which the buyer will presumably receive a series of shipments—perhaps many thousands of tons. It is necessary to make this distinction because coal is a variable material—a heterogeneous mixture of a variety of components—the quality of which will vary from one lot to another. Therefore an absolutely accurate determination of the quality (if that were possible) of one lot of a coal is an