[FRIAM] ATTN: George Duncan

Tue May 26 09:52:44 EDT 2020

Frank,
Indeed!

And yet, that *is* what the concept entails... isn't it?

When we wonder about whether or not a coin is "fair", we wonder if it will
produce an equal number of heads and tails with no pattern if we kept on
flipping it forever. We will need to bring statistics into the discussion
*because*, as you point out, the odds of getting exactly 1/2 on any given
run is small, and because short runs could easily appear to have a pattern.

What we need to avoid is mistaking the concepts wrapped up in the
statistics for the concept we are actually interested in. If we are
interested in "fair", we are not directly wondering about the statistical
probabilities associated with any given run, but rather we are using the
statistics to aid in our inferences regarding the broader concept.

Thus statistics will always feed the inference, never replace it. If we
tested a fair coin long enough, we would eventually expect to get a run of
100 heads. That means that if we tested enough fair coins, one of them
would eventually give 100 heads on the first 100 flips. As such, even
seeing something as unlikely as 100 heads in a row does not definitively
rule out that a coin is fair; we would still be inferring regarding the
(un)fairness.

See also the classic Dilbert comic, attached
[image: Dilbert Random Number.gif]
.

-----------
Eric P. Charles, Ph.D.
Department of Justice - Personnel Psychologist
American University - Adjunct Instructor
<echarles at american.edu>

On Sun, May 24, 2020 at 10:36 PM Frank Wimberly <wimberly3 at gmail.com> wrote:

> "The concept "fair", entails, in its entirety, that the coin will, in the
> long run, produce an equal number of heads and tails with no pattern."
>
> George will correct me and I defer to his greater knowledge of probability
> theory.  I believe a fair coin the distribution of heads/tosses will have
> an expected value of 1/2.  For a large number of tosses the probability of
> an equal number of heads and tails is vanishingly small.
>
> Frank
>
> On Sun, May 24, 2020 at 8:25 PM Eric Charles <
> eric.phillip.charles at gmail.com> wrote:
>
>> Nick,
>> I feel like this fast-forwarded some how. The first and most important
>> thing Perice wants is for us to think clearly about our concepts, right?
>>
>> So, before we get going into this, the first thing we need to do is
>> figure out whether we agree on the following:
>>
>> The concept "fair", entails, in its entirety, that the coin will, in the
>> long run, produce an equal number of heads and tails with no pattern.
>>
>> That is, while we can hypothesize about whether the coin is fair based on
>> all sorts of things - studying how it was made, measuring it's symmetry,
>> etc. - we recognize that any such evidence would be irrelevant in the face
>> of results from a very large number of flips.
>>
>> Phrased the other way around: The claim that a given coin is "fair", if
>> we are thinking clearly, a claim about what result we will see if we flip
>> the coin a very large number of times. Nothing more, nothing less. Though
>> we expect the construction of a coin to impact whether or not it is "fair",
>> we are definitely *not *asserting that it has any
>> particular construction when we assert that it is fair.**
>>
>>
>>
>> ** Note the connection with our prior discussion of psychological terms
>> and human insides.
>>
>> -----------
>> Eric P. Charles, Ph.D.
>> Department of Justice - Personnel Psychologist
>> American University - Adjunct Instructor
>> <echarles at american.edu>
>>
>>
>> On Sun, May 24, 2020 at 2:56 PM <thompnickson2 at gmail.com> wrote:
>>
>>> All, particularly, George—
>>>
>>>
>>>
>>> In an earlier larding, I argued that Peirce’s idea of truth is
>>> essentially a statistical one.   So:
>>>
>>>
>>>
>>> Is it true that the coin I hold in my hand is a fair coin?
>>>
>>>
>>>
>>> Let the coin be flipped once, and it comes out heads, what do you
>>> think?  No way of telling, right? OK.  Flip it again.  Heads again.  Two
>>> heads in a row.  P=0.25.  Sure, I guess so.  It could be fair.  Flip it
>>> again. Hmmm. Three heads in a row………*Five* heads in a row. P= 03125.
>>> You know?  I think that coin is probably not fair.  “Fair” in this
>>> formulation means the infinite distribution of H and T coinflips is .5.
>>> “Probably not” means, the chances that this coin’s flips are drawn from a
>>> .5 distribution is less than 0.0312 and my threshold of dis belief is
>>> 0.05.  Thus, when I  say that the coin is not fair, that inference is in
>>> part a statement about me, and the truth of the matter, the limit of the
>>> distribution of flips, is prospective.  But the notion that there can be
>>> some truths of some matters is absolutely essential to science.  Why else
>>> would we flip the coin?
>>>
>>>
>>>
>>> Now George:  why am I bothering you about this.  Three questions:
>>>
>>>    1. Is this valid statistical logic?  I ask because all psychologists
>>>    are only amateur statisticians, and many of us bugger up the logic. In
>>>    particular, we are known to confuse type I and type II error.
>>>    2. Is this Peirce’s logic?  If not, what is Peirce’s logic; and
>>>    3. Is Peirce’s logic the ORIGIN of the logic of statistical
>>>    inference that I was taught 60 years ago in graduate school**.  If so,
>>>    which among the famous statisticians, Pearson, Spearman, Fischer, etc.,
>>>    read Peirce?
>>>
>>>
>>>
>>> [signed]
>>>
>>>
>>>
>>> TLOLTT*
>>>
>>>
>>>
>>> * The Little Old Lady Tasting Tea
>>>
>>> ** RIP, Rheem Jarrett
>>>
>>>
>>>
>>> Nicholas Thompson
>>>
>>> Emeritus Professor of Ethology and Psychology
>>>
>>> Clark University
>>>
>>> ThompNickSon2 at gmail.com
>>>
>>> https://wordpress.clarku.edu/nthompson/
>>>
>>>
>>>
>>>
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>
>
> --
> Frank Wimberly
> 140 Calle Ojo Feliz
> Santa Fe, NM 87505
> 505 670-9918
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