In applied statistics there is something called a Hypothesis Test, let’s do some unpacking and explain this concept:

Let’s talk about apples, if we were magical, we could study *every single apple* in a split second and know facts about every apple in existence, such as the average weight of Apples. I used capital ‘A’ Apples to emphasize this is the true, actual, average weight based on our magical knowledge of every possible apple. We obviously don’t know what the average Apple weight *really is* so let’s guess. Let’s say it’s 4 ounces.

So we buy a crate of apples – these we can actually weigh – and the average weight of our crate of apples is 5.2 ounces.

So here’s our question – does the fact that our crate of apples has a mean weight of 5.2 ounces *disprove* our Hypothesis that the actual mean Apple weight is 4 ounces? Can we *test this hypothesis?*

I won’t bore you more, but the test boils down how far from the hypothetic 4 ounces our actual 5.2 ounces is, how many apples were in our crate, and how much the weight of one apple varies from others. Based on the variance in apple weights, we can translate the distance between 4 ounces to 5.2 ounces into a percentage likelihood, if the likelihood is small enough, we call Bullshit on the 4 ounce hypothesis and that’s how this all works.

So – the Anderson-Darling test is a hypothesis test that checks if a series of numbers come different kinds of distributions. It functions like a hypothesis test above, you have a claim “These numbers come from a Normal Distribution” and the test with try and prove they don’t. The test also checks for a handful other types of distributions as well.

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