[FRIAM] ATTN: George Duncan

Tue May 26 10:11:45 EDT 2020

Funny.  True but probably irrelevant.

That's a joke.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Tue, May 26, 2020, 7:53 AM Eric Charles <eric.phillip.charles at gmail.com>
wrote:

> 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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