"Eyeball Test" to Identify An Unfair Coin (or A False Record) | /en/2008/09/eyeball-test-to-identify-an-unfair-coin/

yihui 2022-12-16 14:51:32

"Eyeball Test" to Identify An Unfair Coin (or A False Record)

https://yihui.org/en/2008/09/eyeball-test-to-identify-an-unfair-coin/

1 Comment

giscus-bot 2022-12-16 14:51:33

Guest *Kevin* @ 2008-10-08 22:16:04 originally posted:

I think it's actually pretty easy to tell which coin is fair based on the raw data. The first sequence has a string of 10 zeros in a row. The chance of this happening in a sequence of 100 numbers is very small. I once read about a statistics professor who would have some students simulate data with real coins and have other students write down a random sequence of zeros and ones. Using a rule of thumb that real data rarely contains more than a string of seven identical digits (in a string of 100), he could pretty accurately identify the real coin-toss data.

yihui 2022-12-16 14:51:34

Please DO notice the maximum run length in the middle plot! You think 10 zeros must be a rare event at the first glance, but through the simulation (animation), you can observe that long sequences of all 0s or 1s occur very often, which may be contrary to you thought. Numerically you can use "the maximum run length" or "the number of runs" as the statistic to test which coin is unfair.

Originally posted on 2008-10-10 13:15:07