04968nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001300153072001700166072002300183072001600206100007900222245013900301250001800440264006900458300004200527336002600569337002600595338003600621347002400657490007500681505085100756520237901607650004203986650001804028650002704046650009904073650002204172650002704194710003404221773002604255776003604281776003604317776003604353830007504389856004604464978-3-031-70051-4DE-He21320251030113245.0cr nn 008mamaa241025s2024    sz |    s    |||| 0|eng d  a97830317005147 a10.1007/978-3-031-70051-42doi 4aHA1-4737 7aJHBC2bicssc 7aSOC0270002bisacsh 7aJHBC2thema1 aBeltrami, Edward.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aDigressions in Elementary Probabilityh[electronic resource] :bThe Unexpected in Medicine, Sports, and Society /cby Edward Beltrami.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aX, 121 p. 19 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aQuantitative Methods in the Humanities and Social Sciences,x2199-09640 aSuccess Runs in Bernoulli Trials -- Chapter 2. The Remarkable Streak of Joe Di Maggio -- Chapter 3. Inherited, Not Acquired -- Chapter 4. A Subtle Bias -- Chapter 5. Addendum : Conditional Expectation -- Chapter 6. Hot Hands in Basketball -- Chapter 7. Restricted Choice -- Chapter 8. Another Conundrum : What Does Crowd Size at Wimbledon’s Tennis Match Tell us About Baseball Batting Averages?- Chapter 9. Cancer Clusters -- Chapter 10. Medical Mis-Readings -- Chapter 11. The Wrong Conclusion -- Chapter 12. Clinical Trials -- Chapter 13. Margin of Error -- Chapter 14. What Are the Odds of That?- Chapter 15. Turing’s Evidence -- Chapter 16. Bell’s Inequality -- Chapter 17. The Paradox of Random Arrivals -- Chapter 18. The Inverse Square Root Law -- Chapter 19. Runs, Again -- Chapter 20. Addendum : Tutorial on Elementary Probability.  aThis book is about the interplay between chance and order, but limited to mostly binary events, such as success/failure as they occur in a diversity of interesting applications. The goal is to entertain and instruct with topics that range from unexpected encounters with chance in everyday experiences, to significant “must know” insights regarding human health and other concerns in the social sciences. The first section provides the tools for being able to discuss random sequences with hints at what is to follow. This is followed by another surprising and, to some extent, bizarre result known as Stein’s Paradox, which is applied to baseball. The troublesome topic of disease clusters, namely to decide whether the clumping of events is due to chance or some environmental cause, is treated using both the Poisson and normal approximations to the binomial distribution and this leads naturally into a discussion of the base rate fallacy and a case study of hospital performance. Next, another medical case study this time concerning some tricky questions about the effectiveness of colonoscopy and other medical interventions. A brief discussion of the mathematics of clinical trials, follows. Then, the book examines the error in random sampling, when polling for candidate preference with specific current examples. The essential tool here is covariance of random variables. The author follows this with a treatment of the spooky quality of coincidence using appropriate mathematical tools. After this, code breaking at Bletchley Park using Baye’s theorem. It returns to Poisson events to discuss another unexpected result, followed by the use of spatial Poisson events in the delivery of emergency response services. Finally, an account of fluctuations that occur in a run of Bernoulli trials as a bookend to the very first section of the book. The probability theory involved is elementary using the binomial theorem and its extensions to Poisson and normal events in addition to conditional probability and covariance. The author provides an optional brief tutorial at the end, that covers the basic ideas in probability and statistics needed in the main text. Besides a list of references, several codes written in Matlab that were used to illustrate various topics in the text, as well as to support several figures that appear throughout, are provided. 0aSocial sciencesxStatistical methods. 0aStatistics . 0aMultivariate analysis.14aStatistics in Social Sciences, Humanities, Law, Education, Behavorial Sciences, Public Policy.24aBayesian Network.24aMultivariate Analysis.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303170050708iPrinted edition:z978303170052108iPrinted edition:z9783031700538 0aQuantitative Methods in the Humanities and Social Sciences,x2199-096440uhttps://doi.org/10.1007/978-3-031-70051-4