Benford's Law says that many naturally occurring sets of observations follow a certain logarithmic law. Relative frequencies of the first significant digits k are log(1 + 1/k) for k = 1, 2, ..., 9, where the base of the logarithm is ten. Financial and other auditors routinely check data sets against this law in order to investigate for fraud. We present the principal underlying mechanism that produces sets of numbers with the Benford property. Examples in which each observation consists of a product of variables are given. Two standard statistical tests that are useful for testing compliance with Benford's Law are outlined. A new Minitab macro, which implements both statistical tests and produces a graphical output, is presented.
The Digest 35 method is commonly used in specifications to identify aggregates that are likely to produce concrete with high drying‐shrinkage characteristics. However this test is protracted and monopolises equipment for long periods of time. Studies of two variants of a methylene blue dye adsorption test are described. The main findings were: (1) The methylene blue dye adsorption test is simple, inexpensive and rapid. Such a test could provide a screening procedure that would reduce the number of Digest 35 tests needed. (2) With the exception of limestone aggregates, good correlation was found between the results of the dye and the Digest 35 tests. (3) The variant using small single‐sized samples gave the higher adsorption values and yielded a better separation. Using large real‐sized samples gave lower and less well‐separated results; however sampling error would be less and there would be some saving in time. (4) Care would be needed in the specification of a standard dye test because results were found to be sensitive to changes in test conditions.
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