Eric inter alia,
Isn’t that a joke about the presidential campaign of our current housing and urban development secretary, Ben Carson? If ever there were a mantra of Pragmatism it would be: You can never be sure! Nick Nicholas Thompson Emeritus Professor of Ethology and Psychology Clark University <mailto:[email protected]> [email protected] <https://wordpress.clarku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/ From: Friam <[email protected]> On Behalf Of Eric Charles Sent: Tuesday, May 26, 2020 7:53 AM To: The Friday Morning Applied Complexity Coffee Group <[email protected]> Subject: Re: [FRIAM] ATTN: George Duncan 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 . ----------- Eric P. Charles, Ph.D. Department of Justice - Personnel Psychologist American University - Adjunct Instructor On Sun, May 24, 2020 at 10:36 PM Frank Wimberly <[email protected] <mailto:[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] <mailto:[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 On Sun, May 24, 2020 at 2:56 PM <[email protected] <mailto:[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] <mailto:[email protected]> https://wordpress.clarku.edu/nthompson/ -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam <http://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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