Can anyone suggest where to obtain the results of the 10,000 coin flips (i.e., all 10,000 heads and tails) performed by John Kerrich during WWII?

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    $\begingroup$ Given that he was locked up in a Nazi prison at the time, I do wonder if he had enough paper to record all 10k results, or if he only actually wrote down the summary values. $\endgroup$ – Corone Nov 15 '13 at 17:00
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    $\begingroup$ @Corone 10K results could easily be recorded on one standard sheet of paper using, say, a dot and bar code (as in ||||..|....||.|..||. etc). This can be compressed using (for instance) hexadecimal. In the previous example, letting | be 1 and . be 0, the hex representation is f21a6. By writing small but visible characters I can easily fit 50 such characters in one line of writing and 50 lines on a sheet, thereby representing a sequence of 50*50*4 = 10K outcomes. $\endgroup$ – whuber Nov 15 '13 at 17:08
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    $\begingroup$ @whuber haha, yes I started pondering similar things after my comment. I'm doubtful that in the pre-computer era hexadecimal would have sprung to mind as it does now, although octal would still give you a chance. Still I gave it a go and dots and dashes alone I could get more like 100 across a sheet, so if he used both sides 10K would just about fit. Maybe that's why he stopped at 10K! $\endgroup$ – Corone Nov 15 '13 at 22:19
  • $\begingroup$ A Nazi prison, yes, but in Denmark, it was not an extermination camp ... $\endgroup$ – kjetil b halvorsen Mar 17 '15 at 21:13
  • $\begingroup$ @kjetilbhalvorsen - actually a Danish prison camp in Hald with Danish guards etc. to protect the internees from the Germans $\endgroup$ – Henry Aug 16 '18 at 17:34

I hadn't heard about Kerrich before-- what a bizarre story. The Google book scan (shared by reftt) of "An Experimental Introduction to the Theory of Probability" doesn't seem to include the body of the text. Feeling a little old-fashioned, I checked out a copy of the 1950 edition from the library.

I have scanned a few pages that I found interesting. The pages describe his test conditions, data from the first 2000 coin flips and data from the first 500 of a series of 5000 equally implausible-sounding urn experiments (with 2 red and 2 green ping pong balls).

Text recognition (and some cleanup) using Mathematica 9 gives this sequence of 2000 tails (0) and heads (1) from Table 1. The head count of 1014 is one more than 502+511=1013 in Table 2, so the recognition was imperfect, but it looks pretty good--at least it got the right number of characters! (Sharp-eyed readers are invited to correct it.)

Here is a graphical summary of this random walk, followed by the data themselves. The accumulated difference between head and tail counts proceeds from left to right, covering all 2000 results.


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    $\begingroup$ You're welcome. I superimposed a plot of these data on your scanned image, hoping it would make any discrepancies obvious, but I'm unable to find any differences at all. Either there are no errors and Kerrich miscounted or I just cannot find the error, but in any case the data posted here are an accurate text rendering of his Table 1. $\endgroup$ – whuber Nov 20 '13 at 18:16

This presentation shows the data for set intervals of tosses. It also references the primary source from Kerrich.

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    $\begingroup$ The source of the (summary) data in that presentation is Freedman, Pisani, & Purves Statistics (any edition). It is, however, only a summary, not an account of all the results requested here. Kerrich published his results in 1946 in a small book; Google has digitized it. $\endgroup$ – whuber Nov 15 '13 at 16:35
  • $\begingroup$ Like I said, it has data for "intervals of tosses" and the presentation references Kerrich's monograph where he published his results. I don't know if Kerrich published his a list of every single toss. Figured this was at least more helpful than just the overall proportion. $\endgroup$ – user31668 Nov 15 '13 at 17:20
  • $\begingroup$ @whuber: yes, that was the monograph referenced in the presentation. it seems to have limited availability. has anyone found a pdf? $\endgroup$ – user31668 Nov 15 '13 at 17:24

There's another Kerrich reference in the book "Chance encounters: A First Course in Data Analysis and Inference" by Chris Wild and George Seber which says in chapter 4 (can download supplement from this page) that the data are published in Kerrich [1964] and Freedman [1991, Table 1, p. 248]. The Kerrich book is probably An Experimental Introduction to the Theory of Probability, and Freedman is the same textbook already mentioned. I doubt that the 1964 monograph would contain more data than the 1946 one though.


That book of Kerrich can be bought used from Amazon, but the quoted price is rather stiff!

A better option is https://openlibrary.org
You need to make an account there, then install Adobe Digital Editions for reading the book. (seems like no other program will do, the downloaded book have DRM, digital restrictions management). Then you can download ("borrow") the book. I am reading it just now. I guess I can take a screen copy of the pages with the results, and use ocr on that. For later ...

(No I have gone fast through the book, it seems that only the first 2000 tosses are given individually, but there are many diverse tables with summaries of the throws. There are also tables for some other experiments, such as drawing balls from an urn, in the same spirit.

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    $\begingroup$ It's not clear whether you have noticed that the first 2000 individual results are already available in this thread at Bill Bradley's answer. The book appears in Google books; I provided a link in another comment. Currently Google links to other booksellers, in addition to Amazon, where the quoted price (including shipping) is considerably cheaper. $\endgroup$ – whuber Mar 17 '15 at 22:11
  • $\begingroup$ Thanks, I noted the 2000 tosses where available above, but hoped I could find more in the book itself. Seems not. I am not able to read the book via google books, maybe that access depends on geography? By the way, I now returned my loan from openlibrary, so others can try ... $\endgroup$ – kjetil b halvorsen Mar 17 '15 at 22:20
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    $\begingroup$ I attempted the same thing when this thread appeared, with the same negative results. :-( I did not mean to intimate that we can actually read the version on Google books: it is only sort of searchable. GB's main value (at least until Google's policy changes) is in providing links to places where we might purchase it. $\endgroup$ – whuber Mar 17 '15 at 22:23

I came across this when doing some background research on Kerrich. I took the data from Bill Bradley's answer - really appreciate that the data was digitized! I've added the data to the R package that I use for teaching, which is available on GitHub.


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