To test

K

subsequences

u

1

,

u

2

, ...,

u

n

;

u

n +1

,

u

n +2

, ...,

u

2n

; ...;

u

(K-1)n+1

,

u

(K -1)n+2

, ...,

u

Kn

of the original sequence, p-values

p

1

,

p

2

, ...,

p

K

are computed. Since the resulting p-values for the sequence

u

1

,

u

2

, ...,

u

Kn

of truly random numbers are supposed to be uniformly distributed over the interval  (0, 1), a uniformity test can be performed for these p-values, returning p-value

q

1

of the second level. Repeating this procedure

L

times results in obtaining

L

p-values of the second level

q

1

,

q

2

, ... ,

q

L

on which you can perform threshold testing.

We have conducted threshold second level testing for the VS generators with ten iterations (

L

=10) and applied the Kolmogorov-Smirnov goodness-of-fit test with Anderson-Darling statistics to evaluate

p

1

,

p

2

, ...,

p

K

uniformity.