Quality Tests of Final Generator

Each line lists a separate test and its result. The result of each test is expressed as a value of Chi-squared Probability.

A Chi-squared Probability should range uniformly between 0 and 1; any value within the range is acceptable. Values too close to either edge, however, are suspect. A reasonable cut-off for success is being farther from an edge than about one part per thousand, or 0.1%. This is the value that is used to determine whether a test passes or fails.

This statistic reflects the how well or badly the measured data correspond to our conjectured equation for the underlying operation. In practice, when the hypothesized equation is wrong, these values of probability will be "off the charts". They can be a hundred orders of magnitude less than zero, for example.

Processed 10,000,000 Random Numbers:

 1.) Frequency    Test PASSED, Chi-squared Probability = 0.102161
 2.) Serial       Test PASSED, Chi-squared Probability = 0.334394
 3.) Gap          Test PASSED, Chi-squared Probability = 0.290057
 4.) Poker        Test PASSED, Chi-squared Probability = 0.689887
 5.) Coupon       Test PASSED, Chi-squared Probability = 0.092706
 6.) Permutation  Test PASSED, Chi-squared Probability = 0.545439
 7.) Runs         Test PASSED, Chi-squared Probability = 0.049891
 8.) Maximum      Test PASSED, Chi-squared Probability = 0.032209
 9.) M-tuple      Test PASSED, Chi-squared Probability = 0.319140
10.) Birthdays    Test PASSED, Chi-squared Probability = 0.346728

Seed time:   0.035802 seconds;  
Test time: 252.425891 seconds; 2.52426e-05 sec/rand.

These tests were performed on a Pentium-4, 2.8 GHz.

What each test checks is described in the Randomness Tests page.

The full set of tests on all the individual components can be found on the Component Validity Tests page. In addition, we show multiple runs over the quality tests, as one should want to see the Chi-squared probability value ranging freeing between 0 and 1 in separate runnings. If it were to be consistently near 0 or 1, then that would be bad.

Perhaps of interest might be to see some example generator functions which actually fail these validity tests. This study can be found at the Bad Generators page.

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