Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math challenge)

[Ian Sefton <I.Sefton@physics.usyd.edu.au>]

On 21/02/2014, at 12:49 AM, Jeffrey Schnick wrote:

> > So far the only general law of human behavior we've seen asserts that
> > people "religiously avoid" consecutive numbers when cooking up numbers ...
>
> I wouldn't call it a law but I was operating on the hypothesis that in trying to cook up a random distribution of numbers people tend to shy away from nice round numbers like 10, 20, and 30.
> ...


I was thinking along the same lines (although I think "religiously" is a bit of an exaggeration). 
So I used the good old chi-squared null-hypothesis thing to check out the following hypotheses:
 
1) People will tend to avoid numbers evenly divisible by 5 (which includes the next case)
2) People will tend to avoid numbers evenly divisible by 10.
3) People may be biassed in favour of (or against) primes.

I also checked a couple of other ideas but did not discover anything.

 Results:
1) List 1: p = 0.0034; list 2: p = 0.81. We may be on to something here.

2) List 1: p = 3.560E-06 (wow!); but wait for it ...  list 2: p = 0.019 (which lies within the traditional 5% boundary).
 
3) Exactly the same distribution of primes/non-primes occurred  in both sets but there is nothing to get excited about;  p = 0.69 in both cases.

Given that only one of the data sets was generated by people alone, I'm betting that was list 1. I am also suspicious that the generator of list 2 may not be truly "random". 

Cheers
Ian