Re: Randomness Test

*To*: mathgroup at smc.vnet.net*Subject*: [mg58036] Re: Randomness Test*From*: Torsten Coym <torsten.coym at eas.iis.fraunhofer.de>*Date*: Thu, 16 Jun 2005 06:43:54 -0400 (EDT)*References*: <d8oul6$a$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Dave miller wrote: > Okay, I have a sequence of numbers as below. When i do a scatter plot, there seems to be a bias toward positive numbers. Although when I run some tests like "runs test", it shows me that the numbers are random. If that is the case, then when i plot the numbers on a scatter plot, should'nt they be equally divided up and below the x axis? My goal is to prove that that there is a significant bias towards positive numbers. > > > -0.164971751 > 1.137014315 > 0.622389791 > 0.048958333 > 1.232944503 > 0.3241877 > 0.1015 > 0.075538717 > 0.265537849 > -0.175252257 > 0.279807692 > -0.409979424 > 0.628232355 > -0.137667494 > 0.210711568 > -0.984059857 > -0.016778523 > 0.384063745 > 0.079707844 > -0.183936235 > -0.567394095 > 0 > 0.277777778 > 0.785185185 > 0.267555556 > 0.078717201 > 0.344352617 > 0 > 0.442245021 > 0.310665658 > 0.788764045 > 0.015850552 > -0.054098361 > 0 > 0 > 0.929482371 > 0.278787879 > 0.123773346 > 0.125175809 > 0 > 0 > Dave, try the following: x={you list goes here} ListPlot[Abs[Fourier[x]]] Sequences of gaussian distributed numbers (mu=0) have a flat frequency spectrum. Your data shows a significant peak at the first Fourier coefficient, which (spoken in terms of electrical engineering) refers to the DC level. Your data seems to be biased, around Mean[x]=0.182068. Torsten