Re: Prove that Randomness Exists?

chris thompson wrote:
On Nov 19, 4:34 am, Robert Carnegie <rja.carne...@xxxxxxxxxx> wrote:
On Nov 19, 3:40 am, chris thompson <chris.linthomp...@xxxxxxxxx>
wrote:



On Nov 18, 8:49 pm, tgdenn...@xxxxxxxxxxxxx wrote:

On Nov 18, 6:47 pm, chris thompson <chris.linthomp...@xxxxxxxxx>
wrote:

On Nov 18, 12:39 pm, tgdenn...@xxxxxxxxxxxxx wrote:

On Nov 18, 10:35 am, chris thompson <chris.linthomp...@xxxxxxxxx>
wrote:

On Nov 18, 9:02 am, Free Lunch <lu...@xxxxxxxxxxxxxx> wrote:

On Sun, 18 Nov 2007 05:47:05 -0800 (PST), in talk.origins
chris thompson <chris.linthomp...@xxxxxxxxx> wrote in
<8838b99c-70e2-42f5-b2ad-942e8431a...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>:

On Nov 18, 5:45 am, nos...@xxxxxxxxxxxxxxxx (J. J. Lodder) wrote:
chris thompson <chris.linthomp...@xxxxxxxxx> wrote:
On Nov 17, 11:40 am, nos...@xxxxxxxxxxxxxxxx (J. J. Lodder) wrote:
chris thompson <chris.linthomp...@xxxxxxxxx> wrote:
On Nov 16, 5:21 am, nos...@xxxxxxxxxxxxxxxx (J. J. Lodder) wrote:
chris thompson <chris.linthomp...@xxxxxxxxx> wrote:
On Nov 15, 4:27 pm, nos...@xxxxxxxxxxxxxxxx (J. J. Lodder) wrote:
chris thompson <chris.linthomp...@xxxxxxxxx> wrote:
[massive snippage]
If something is random, it isn't biased. That's it.

That is a common misunderstanding.
Trows with a coin that comes up heads 51% of the time
are still perfectly random.
The binomial distribution describes them,

Jan

Where did I indicate that something like 51-49 in a coin toss isn't
random? I never even implied that at all. What on earth makes you
think there's a bias there?

More importantly, there's nothing in what I wrote that should have led
anyone to think I was saying there was a bias there.

It is standard usage to say that a 50-50 coin is fair,
and a 49-51 biassed,

Jan

So your contention is that if I flip a coin 100 times and the result
if 51 heads and 49 tails, the coin is biased?

No, that's just your misunderstanding,

Jan

It followed naturally from what you wrote. If that isn't what you
meant, could you please explain your meaning in some greater detail,
so understanding is facilitated?

You might have added the % signs for yourself?

Jan

OK. I flip a coin 100 times and the result is 51% heads and 49% tails.
Is the coin biased?

Chris

There is no enough evidence to say that it is.

But J.J. Lodder won't explain what kind of evidence he needs to
declare the coin biased. He wrote "50-50" and "51-49", then chided me
for not including percentage marks. So I put them on. He types
sentences with a bare minimum of information, then says it's the
readers' fault for misunderstanding him.

Chris

But the problem with this topic is that we are really always talking
about confidence levels.

If you give me a coin and say it is designed to flip 50-50, I will not
disbelieve you based on 10 flips. But when you get into the millions
of flips, my confidence in your prediction will decline radically, and
I will depend on the history rather than your word. And of course I
will act accordingly, if I am placing a bet on the next flip for
example.

When we talk about radioactive decay, we are not able to do millions
of trials on the same nucleus, and so our confidence relies on theory
and experience with large numbers of what we believe to be identical
entities.

In either case, a small sample size (trials, number of atoms)
decreases our confidence in the outcome relative to other available
information. But how we decide to proceed is going to determined by
the risk/benefit associated with the decision. Perhaps JJ will offer
some of the tests he would use in his judgements.

-tg

At this point I am more interested in Jan Hidders' reconciliation of
random and bias coexisting side by side, rather like the lion and the
lamb, as it were. We all know how that scenario ends. Maybe these guys
should have had a better lawyer:

I think you are looking for certainty in an uncertain world.

Me? I don't think so. The world looks great in gray.

But to go back to my original question---what is your definition of
random? If you define it as equal odds for each of the possible
outcome, that is fine.

Nonsense. That's not fine. A pair of standard dice is random, but they
sure don't have 11 outcomes with equal probabilities.

JJ is using the abbreviated form of rrandom (or
perhaps rrrandom) when he says random. Both rrandom and rrrandom allow
the simultaneous existence of bias. Unfortunately, people are always
dropping the r's, which can be confusing.

-tg

I stand by what I wrote before: if something is random it isn't
biased. And before you ask, bias means a significant (say p=0.05) and
systematic departure from the probability distribution of the
population. So JJ might have been correct if he had answered my
question about the 51-49 coin toss if he had talked about (as you did)
sample size of confidence limits. That's why I asked the questions I
did. Either he didn't feel like answering or...who knows. But to say,
as Jan Hidders did, that you can have a coin that consistently gives
more heads than tails over many trials, and it is still "largely a
random process", is just out in left field.

If we're talking about tossing a coin, a metal disc, in the air,
rapidly rotating, and then catching it, interrupting the rotation, I
find it difficult on reflection to see how that can be something other
than fifty-fifty. If it's a magnetic coin in a strong magnetic field,
perhaps. If you let it bounce on the floor... the face on one side
must have a very large nose, so the coin bounces off that. Or perhaps
the teller has a stammer, sometimes fails to get out the word "heads"
or "tails" - differentially - and throws again to cover his confusion.

The technique doesn't matter in this case. It's a hypothetical case to
explore the meanings of bias and random in a simple model.

But apart from the paradox applied to this particular experiment...
I incline to see the pair of dice "biased" to prefer totals 6, 7, 8,
over 2, 3, 11, 12. But you seem not to allow that. Dice can be
loaded, however; how do you categorise that?

A pair of dice is not biased to 7: it has a natural distribution that
lends a higher probability to 7 than any other outcome. Loading the
dice- say, in favor of the house, so that 2 or 12 comes up more
frequently- introduces bias.

I'm still not getting the distinction. Don't loaded dice have a
"natural distribution" that just isn't the one that you expect? I
think you're discriminating between the "fair" distribution that a
probability experiment "ought" to have and the imperfect real-world
case, but who but God can be saying what's the "fair" ideal case that
the universe isn't living up to? Real things are what they are.

.

Relevant Pages

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  • Re: Prove that Randomness Exists?
    ... Trows with a coin that comes up heads 51% of the time ... anyone to think I was saying there was a bias there. ... disbelieve you based on 10 flips. ...
    (talk.origins)
  • Re: how to determine sufficient sample size?
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