Cochran's theorem

Okay, imagine you have a bunch of marbles in a bag. You want to know something about the marbles, like maybe what percent of them are blue. But you can't look at all the marbles in the bag because there are too many. So you decide to take a sample, which means you reach in the bag and grab some marbles without looking.

Now, you want to know how accurate your sample is, meaning how likely it is to be close to the truth about all the marbles in the bag. Cochran's theorem is a way to help figure that out.

First, you need to know how big your sample is. Let's say you grabbed 20 marbles out of the bag. Cochran's theorem says that the accuracy of your sample depends not just on the number of marbles you took, but on how different the marbles are from each other. If most of the marbles in the bag are blue, and you end up with a sample that is all red, then your sample isn't very accurate even if you got 20 marbles.

So, Cochran's theorem helps you calculate how accurate your sample is based on how different the marbles are from each other and how big your sample is. It's like a special tool that helps you make sure you're not guessing too much about what all the marbles in the bag look like based on just a few you grabbed.