----- Original Message -----
From: Jan de Leeuw <[EMAIL PROTECTED]>
To: Ron Bloom <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Thursday, July 20, 2000 7:00 PM
Subject: Re: Why quote *both* Odds Ratio and Chi^2 ?
> This is one of the areas in which we cannot be precise enough. An
> observed statistics is not a random variable, but
> a realization of a random variable. Random variables
> are theoretical or mathematical constructs, which are never observed
> directly. In frequentist statistics the random variable corresponds with
the
> framework of (hypothetical) replications, in Bayesian statistics
> with the (equally hypothetical) subjective beliefs.
>
> Thus observed statistics do not have sampling distributions, the
> corresponding random variables (of which we assume the statistics
> are realizations) have sampling distributions, where the "sampling"
> usually refers to a theoretical framework of repeated independent
> trials.
.........................................................................
Replication is a theoretical construct in itself, when measuring the
physical universe. Every measurement involves a system, which includes
equipment or tools for the measurement, the environment or conditions at the
time of an event, and a process of reducing the observed event to a value
using the equipment.
I may be able to repeat the event, (i.e. generation of a nanosecond pulse),
and get a different extent of reaction (i.e. the realization) , but cannot
distinguish the source of randomness as to whether it comes from the process
of measurement, from the randomness of the conditions of the environment, or
it is of the event itself.
Therefore I have to assume either that the event is the random variable, or
the environment is the random variable, or that the measurement is the
random variable. It is clearly dependent on what my hypothesis is, which is
itself a mathematical construct from an assumed physical theory.
It is the problem of understanding what a replication is (outside of card
and dice games) and the probability of different realizations that makes it
so difficult to fit statistical theory to practical applications. This is
very true when replications are impossible. The probability structure at
this point is very arbitrary. Therefore it hard to challenge any approach.
DAHeiser
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