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Re: CLT and "ramdomness"



Quoting Bernard Cleyet <anngeorg@PACBELL.NET>:

If I read my stats. pamphlet correctly the CLT ensures combined multiple
error sources fits a Gaussian. If one tabulates data from a clock timer
(measures the time between ticks) and it fits a Gaussian, can one assume
it is random and not systematic?

In general, no.

1) As a point of logic, just because random => gaussian
doesn't give us any confidence that gaussian => random.

2) As a point of fact, counterexamples abound.

3) More generally (with apologies to Dykstra) I like to say:
-- testing can certainly prove the absence of randomness
-- testing can never prove the presence of randomness

Testing for adherence to the central-limit tendency is not
even a very strong test.

For a discussion of these issues, including a theoretical
analysis and a zero-cost ready-to-use source of industrial-strength
random numbers, see
http://www.av8n.com/turbid/paper/turbid.htm