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> be careful if you do it 20 times

Probably just a locution, but be careful with that idea about numbers:

The probability of remaining in a safe zone of 95% for 20 consecutive times is ~36%. It ( (1-(1/n))^n ) approximates to 1/e.

The number of tries to reduce that 95% to a 50% coin toss is 13. It is not fully intuitive. One will put his threshold wherever one may think appropriate, but. A chance of tenth, a hundredth, a thousandth etc. for ten, a hundred, thousand etc. times approximates to 63.2%.

...Maybe a locution like 'Maybe 9 out of 10 times you'll be fine, but be careful about doing it 7 times' could work well (as 6.931 approximates the risk to a coin toss).



NB: This failure of statistical logic also shows up in "100 year storm" statistics.

The actual measurement is "storm with a 1% likelihood of occurring in any one year". The odds of that storm occurring in a century is actually about 63%, and of occurring in any ten year period, about 10%.

Add to that the fact that the measurement is based on a storm of a given magnitude (usually total rainfall / precipitation, wind speed, storm surge, etc.) occurring, and small changes in the likelihood of such events can dramatically change the rate at which a storm of a given magnitude is observed. If you live in/near flood-prone areas, keep an eye on, e.g., changes in what are considered flood stages (say, as flood control structures are added or removed), or to likelihoods of events of a given precipitation level or stream height.


So that explains the seven lives of cats, who 9 times out of 10 land on their feet. (Also, 85% of statistics are made up on the spot.)




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