# Solved – Chi squared test for randomness

I am testing pseudo-random number generators and need to perform a chi-squared test. However, I've encountered some difficulties.

Let's take the following example: I have generated 100 numbers, ranging from 1 to 10.
The distribution is as follows:

1: 8

2: 12

3: 9

4: 11

5: 16

6: 6

7: 8

8: 10

9: 13

10: 7

From what I was able to understand, next I should calculate D.

\$\$D = d1 + d2 + d3 + … + d10.\$\$

\$di =\$ square of the difference between the expected value and the observer value, everything over the expected value

\$\$d1 = ((8 – 10)^2)/10 = 4/10\$\$

\$\$d2 = ((12 – 10)^2)/10 = 4/10\$\$

.
.
.

\$\$d10 = ((7 – 10)^2)/10 = 9/10\$\$

Adding them up results in 84/10 or 8.4.

The next step is comparing this to \$X^2\$.

That is \$X^2[1-alpha,k-1]\$. It is clear that \$k=10\$. But what value should I use for \$alpha\$? And how to I know the value of \$X^2\$ after I decide what \$alpha\$ I am going to use?

It feels that I am close but I just can't figure it out.
Many thanks.

Contents

These critical values can be computed in for example `R` via
``> qchisq(.95,9) [1] 16.91898 ``