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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? 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!
You're saying that statistical significance tests only hold in a controlled laboratory environment. Wow.
If that's true, then we'll never know whether the ICTY was biased. In fact, we'll never know that is was NOT biased.
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.
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.
There are other ways to do it, and there are conditions under which that assumption can be relaxed.
So what's the most appropriate method?
I have to run now, but if you'd like, I can play around with a couple of different measures when I get home, to see what comes out.
In addition, the t-test requires equality of variances as Jake pointed out. The t-test for equality of means is a sad example of a test that is taught because it can be done in closed form on a blackboard rather than because its conditions actually obtain in real life. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
It is not at all obvious that the ratio of indictees to civilians in that case should follow any given distribution, for instace a Gaussian. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
All members of the ethnic group in the whole former Yugoslavia? In the relevant republic? The number of combatants? Or would you expect the number of indictees to be independent of the size of the ethnic group? How about proportionality to the number of dead civilians in other factions, etc?
All this for an unbiased court. You can then quantify the deviations from the model. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
You'd probably end up with a test for the parameter of a Poisson distribution or something, not a mean and standard deviation of a Gaussian. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
And then you can do a test for the rate of conviction which is a Bernouilli test. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
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