I'm really rusty at statistics and I'm trying to write some C# code where I feed in a list of numbers and it tells me whether or not the numbers are normally distributed. I generated 50 numbers from the following site with a mean of 0 and a variance of 1.
http://www.random.org/gaussian-distributions/?mode=advanced
The algorithm I'm trying to use is the Anderson-Darling test (http://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test). I implemented
A^2 = -N - 1 / N * sum(1, N)( (2*i - 1) * (ln Phi(Y[i]) + ln (1-Phi(Y[n+1-i]) ) ) )
(It's about half-way down the page, the case where the mean and variance are both known.)
The Phi function comes from http://www.johndcook.com/csharp_phi.html
When I run the code I wrote on an actual normal distribution, I get a value of -3.05 back.
Is the next step to look this number up in a table of normal distribution critical values to get the associated probability? -3.05 maps to 0.0011. Does this mean that my data has a .11% chance of coming from a normal distribution (assuming my code is correct)
Best Answer
The next step is to compare your value to a critical value for the test-statistic. From the same Wikipedia page:
Meaning, your null hypothesis is that the data are generated from a normal distribution, and an $A^{*2}$ exceeding the critical value implies non-normality at that level of significance. But, the $A^{*2}$ statistic for a normal distribution is not itself normally distributed, per this resource:
The same source points to books and papers for these critical values. Perhaps you might be able to find CDFs for each $A^2$ statistic, and implement the p-value.