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Old August 19th 05, 06:45 PM
Reg Edwards
 
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Default 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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