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.
For the most part, statistical analysis has, in practice, been much more concerned with finding regularities in data as opposed to testing for randomness.
Stephen Wolfram used randomness tests on the output of Rule 30 to examine its potential for generating random numbers,[1] though it was shown to have an effective key size far smaller than its actual size[2] and to perform poorly on a chi-squared test.
[3] The use of an ill-conceived random number generator can put the validity of an experiment in doubt by violating statistical assumptions.
These include measures based on statistical tests, transforms, and complexity or a mixture of these.
The use of Hadamard transform to measure randomness was proposed by S. Kak and developed further by Phillips, Yuen, Hopkins, Beth and Dai, Mund, and Marsaglia and Zaman.