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Off topic. Statistics.
Having temporarily run short of suitable radio topics to write programs about, I came across an older program of mine which people of your intellect might be inerested in. Play with. Or use even. Program HYPERGEO(metric) solves an extremely wide range of important statistical problems. Basically, it is involved with "The Significance of the Difference Between Two Proportions". Input data is in the form of a so-called 2-by-2 Contingency Table. Just 4 numbers. EXAMPLE 1. Manufacturing Quality control. We take a relatively small random sample of N1 widgets from a large batch of widgets and find that a number D1 of them are defective. We then take a relatively small random sample N2 from another manufacturer's large batch and find that that a number D2 of them are defective. The question arises, which manufacturer's product has the highest quality. Bear in mind it is expensive and time-consuming to 100 percent inspect both batches. It may be agreed in advance to inspect only a few percent of the batch sizes or just a fixed number regardless of batch size. So we are obliged to ask the question - from the two samples, is one manufacturer's quality REALLY better than the other? By how mutch is it due to the random selection of a relatively small number of individual widgets from a batch? Probabities are clearly involved. EXAMPLE 2. Medicine and Health of Populations. There has been an epidemic. A fraction of the population were innoculated against it. Out of a sample of people who have been innoculated a number N1 did not suffer from the disease but a number N2 did suffer and die. Out of a sample of people who were NOT innoculated a number N3 were not affected by the disease but a number N4 suffered and died. The question arises, how effective was the innoculation? It may possibly have had adverse affects. The answer is a matter of probability statistics. International Pharmaceuticals please note. There must be other applications in the relatively narrow field of radio communication, perhaps involving the randomness of noise, crosstalk and interference. 2-by-2 Contingency Tables, just waiting for analysis, arise all over the place. Anyone further interested can look up the works of Sir Ronald Arthur Fisher. For example, a collection of his works can be found in - "Statistical Methods, Experimental Design and Scientific Inference". An international master, Fisher was involved with the fields of statistics, agriculture, genetics, mathematics, engineering, biology, medicine, etc. Before the age of electronic computers he devised new statistical tables such as the F-Distribution for ANOVA. He died in 1962. Fisher's writings are works of logical plain simple English. The maths are few and don't get in the way. Like Heaviside, a revolutionary. His opinions of earlier workers are scathing. After many years of haggling between prominent statisticians about the correct interpretation of the apparently simple 2-by-2 Contingency Table, it was Fisher's logic which ended the arguments. Despite its simplicity, the numbers involved in the probability calculations are so large it is necessary use their logarithms to prevent numerical overload of ordinary computers. Within the next few hours I'll make program HYPERGEO available from the following website. It would be a pity should it be lost. ---- .................................................. .......... Regards from Reg, G4FGQ For Free Radio Design Software go to http://www.btinternet.com/~g4fgq.regp .................................................. .......... |
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