Stephen Wolfram used randomness tests on the output of Rule 30 to examine its potential for generating random numbers, though it was shown to have an effective key size far smaller than its actual size and to perform poorly on a chi-squared test. For example, the infamous RANDU routine fails many randomness tests dramatically, including the spectral test. These generators do not always generate sequences which are sufficiently random, but instead can produce sequences which contain patterns. The sequences they produce are called pseudo-random sequences. Many "random number generators" in use today are defined by algorithms, and so are actually pseudo-random number generators. For the most part, statistical analysis has, in practice, been much more concerned with finding regularities in data as opposed to testing for randomness. Tests for randomness can be used to determine whether a data set has a recognisable pattern, which would indicate that the process that generated it is significantly non-random. The issue of randomness is an important philosophical and theoretical question. If a selected set of data fails the tests, then parameters can be changed or other randomized data can be used which does pass the tests for randomness. In some cases, data reveals an obvious non-random pattern, as with so-called "runs in the data" (such as expecting random 0–9 but finding "4 3 2 1 0 4 3 2 1." and rarely going above 4). In stochastic modeling, as in some computer simulations, the hoped-for randomness of potential input data can be verified, by a formal test for randomness, to show that the data are valid for use in simulation runs. A randomness test (or test for randomness), in data evaluation, is a test used to analyze the distribution of a set of data to see if it can be described as random (patternless).
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