In reading about the 2-sample KS test, I understand exactly what it is doing but I don't understand why it works.
In other words, I can follow all the steps to compute the empirical distribution functions, find the maximum difference between the two to find the D-statistic, calculate the critical values, convert the D-statistic to a p-value etc.
But, I have no idea why any of this actually tells me anything about the two distributions.
Someone could have just as easily told me that I need jump over a donkey and count how fast it runs away and the if the velocity is less than 2 km/hr then I reject the null-hypothesis. Sure I can do what you told me to do, but what does any of that have to do with the null-hypothesis?
Why does the 2-sample KS test work? What does computing the maximum difference between the ECDFs have to do with how different the two distributions are?
Any help is appreciated. I am not a statistician, so assume that I'm an idiot if possible.