There should be more to testing the randomness of a draw that what Kevin describes below.

Problems that may not be identified using the approach below are:

* Periodicity * Second and higher order correlations between observations

A quote from NIST suggests the following tests need to be run to certify a random number generator:

(Cited from http://www.itl.nist.gov/div898/pubs/ar/ar1998/node6.html )

Many statistical tests exist that determine specific kinds of nonrandomness. These include: (1) Frequency tests, to verify that the proportions of zeroes and ones are equal; (2) Runs tests, to verify that the binary sequence doesn't alternate too frequently, or contain too many or too few long substrings of zeroes or ones; (3) Spectral tests, that look for periodicity in the local frequencies of zeroes and ones (an extension of this test based on wavelet analysis looks for aperiodic variation in these frequencies); (4) Geometric tests, which can look at how often a random walk based on the sequence returns to the origin, or at the local dimensionality of n-tuplets of numbers built from the sequence, and other theoretical properties of multivariate spacings; (5) Compression tests, that use complexity theory to estimate if a sequence compresses too much, indicating that some kind of patterning is present. We have developed a large suite of these tests, together with the associated mathematical theory, critical values, and guidelines for application, so that any user will be able to assess the strength of their own encryption algorithms.

NIST tests for randomness can be downloaded (for UNIX) at http://csrc.nist.gov/rng/rng2.html

Warren Schlechte

-----Original Message----- From: kviel [mailto:kviel@GMCF.ORG] Sent: Thursday, July 12, 2001 8:21 AM Subject: Re: testing for randomness of a sample

Regi,

The draws will have a distribution. The expected value of the mean and variance of a series draws of size N should approach the mean and variance of the underlying population. This could be the basis for a statistical test. I would assume that this is not possible for one draw, meaning many draws are in order. You may even be able to invoke the CLT.

Another possibility is to examine the method employed to obtain the sample.

Regards,

Kevin

PS Dale McLerran has posted a SAS macro for a random draw from a SAS data set previously to this list.

-----Original Message----- From: Mathew, Regi (CAP, CARD) [mailto:Regi.Mathew@GECAPITAL.COM] Sent: Wednesday, July 11, 2001 5:40 PM To: SAS-L@LISTSERV.UGA.EDU Subject: testing for randomness of a sample

Hi SAS-L:

We are testing various functionalities of a software. One of the functionality of the software is 'random selection'. It allows us to draw random sample from a population (user decides the proportion). How can we test that the sample is indeed random? Is there a specific test for it?

Thanks for you response.

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