Hi, Bill! Thanks for your comments.
> MP>In some sense I did it when I compared a single event (the coin toss)
> and the collective outcome (the frequency distribution). However, I am
> not
> sure if there is such distinction. Both are generated by the same
> processes.
>
> bw> I am no scientist but I think your last two sentences above are very
> important. It is like the error claiming a cause and effect between sets
> of data without hard evidence of the relationship.
[...]
> In the same way, there is a vast philosophical and theoretical difference
> between probability and statistics, yet they are generated by the same
> processes. Statistics only applies to past events-historical data while
> probability only applies to future events - stuff which has not yet
> happened. It is not proper to refer to the probability of a past event.
> sort of like a division by zero - it can be written but not interpreted
> (by most people - probably not saying any of this right).
I understand your point about a difference between statistics and
probability. However, I don't see how it relates to establishing
cause-effect relationships without hard evidence.
Also, I might be wrong, but it seems to me that scientists usually don't
use this distinction between probability and statistics while using an
hypothetical-deductive method. Imagine an experiment to test the effect
of some drug. They would use probability to establish the working and the
alternative hypothesis, but afterwards they would analyse the results
using statistics. If the distiction you suggest is really important in
this case, someone could say that they can't really state anything
about the outcome of the experiment because it is a "historical
singularity" and all one could say about it (mathematically) is that it
happened.
Marcio
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