Because of their relative size? Because they were precisely different wars? Why?

Because of their relative size. All other things being equal, smaller numbers have larger relative uncertainties - and relative uncertainties go into multiplication and division. So when you divide two small numbers, than you get a larger uncertainty on the ratio than when you divide two large numbers.

So you're saying that a statistical significance test requires that all data points used have the same level of uncertainty in order to hold?

Not all significance tests, just the one you're using. The one you're using assumes Gaussian distributions with uniform uncertainties. There are other ways to do it, and there are conditions under which that assumption can be relaxed, but the way you're doing it isn't one of those conditions.

That means that you can't calculate statistical significance of the output of one factory compared to another - larger one... of one assets price to that of another - traded by a different bank... of one petri dish to another - not manufactured by the same company!

Yes you can. But not the way you do above.

You're saying that statistical significance tests only hold in a controlled laboratory environment. Wow.

No, I'm saying that the test you're using above only holds when you have (roughly) equal uncertainties, which you don't have. That's more likely to be a reasonable approximation in a controlled lab environment, but when you have independent means to estimate the uncertainties involved (as is usually the case in the real world, you can modify the test to deal with that.

- Jake

Friends come and go. Enemies accumulate.