where

and is the sample variance. If 's are uniformly distributed, , . Then we have .

In practice, we do not calculate directly; instead, an estimate of
can be obtained by just plugging , , , into
following formula as shown in [10]:

where . If we further assume that 's are independent, then we have

Under the null hypothesis that (independence), the following statistic has an approximate standard normal distribution

The hypothesis will be rejected at significance level if . is the distribution function of standard normal distribution.

In this project we have tested up to 10-lag autocorrelation of each RNG.