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 <[email protected]> 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 > <[email protected]> > > > On Sun, May 24, 2020 at 10:36 PM Frank Wimberly <[email protected]> > 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 < >> [email protected]> 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 >>> <[email protected]> >>> >>> >>> On Sun, May 24, 2020 at 2:56 PM <[email protected]> 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 >>>> >>>> [email protected] >>>> >>>> https://wordpress.clarku.edu/nthompson/ >>>> >>>> >>>> >>>> >>>> -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. >>>> . ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... >>>> FRIAM Applied Complexity Group listserv >>>> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam >>>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >>>> archives: http://friam.471366.n2.nabble.com/ >>>> FRIAM-COMIC http://friam-comic.blogspot.com/ >>>> >>> -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . >>> ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... >>> FRIAM Applied Complexity Group listserv >>> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam >>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >>> archives: http://friam.471366.n2.nabble.com/ >>> FRIAM-COMIC http://friam-comic.blogspot.com/ >>> >> >> >> -- >> Frank Wimberly >> 140 Calle Ojo Feliz >> Santa Fe, NM 87505 >> 505 670-9918 >> -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . >> ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... >> FRIAM Applied Complexity Group listserv >> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam >> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> archives: http://friam.471366.n2.nabble.com/ >> FRIAM-COMIC http://friam-comic.blogspot.com/ >> > -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . > ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC http://friam-comic.blogspot.com/ >
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