Result Interpretation

• $\chi ^2$ test: If the result is greater than $\chi_{4095,0.9}=4211$, the RNG fails the test at significance level $\alpha=0.1$.

• KS test: If the result is greater than $c_{0.9}=1.224$, the RNG fails the test at significance level $\alpha=0.1$.

• Collision test: If the result deviates from 128 too much, like several thousands, the RNGs fails.

• Permutation test: If the result is greater than $\chi_{8!-1,0.9}=\chi_{40319,0.9}= 40683$, the RNG fails the test at significance level $\alpha=0.1$.

• Runs-up and Runs-down test: If the result is greater than $\chi_{6,0.9}=10.645$, the RNG fails the test at significance level $\alpha=0.1$.

• Lag-$k$ Autocorrelation: If the absolute value of the result is greater than $\Phi^{-1}(0.95)=1.645$, the RNG fails the test at significance level $\alpha=0.1$.

• Coupon Collector's test: If the result is greater than $\chi_{18,0.9}=25.989$, the RNG fails the test at significance level $\alpha=0.1$.

• Birthday Spacings test: If the result is greater than $\chi_{17,0.9}=24.769$, the RNG fails the test at significance level $\alpha=0.1$.

• Spectral test: If the results deviate from the theoretical value too much, the RNGs fails. (See Section 4.8)