# Solved – When does a random test fail

I must implement some Chi Square Test to test the randomness of "my" implementation, but I can't understand what this tests really say.

The tests are different but what I always do is: divide in different categories, calculate the probability to fall in these categories and then calculate this number:

\$v = sum_{i=0}^{k} frac{(x_k – p_k)^2}{p_k}\$

Where k is how many categories are, \$x_k\$ is how many elements in kth category I've counted and \$p_k\$ is probabily of the kth category multiplied by the number of total instances.

I know that \$v\$ should be distributed like \$chi^2\$ of \$k-1\$ freedom degree; so i calculate many \$v\$ and see where they are.
For example I see that almost 80% is in \$(chi^2_{.10}, chi^2_{.90})\$. But then? What can I say?

For example this is an output of one of my test:

``Test Gap:    Categories: 11. Freedom Degree:  10. Gaps: 10000. Iterations: 10000.   [.10,.90): 8017.              Expected :8000.0   [.01,0.05)U[.95,.99): 772.    Expected :800.0   [.05,0.10)U[.90,.95): 1000.   Expected :1000.0   [0,0.01)U(.99,1]: 211.        Expected :200.0 ``

I know that I cannot say "This is true randomness!", but.. well, can I say that I passed the test? Why? Should I repeat the test other times and…?

Thank you!

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