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Your three data points do not have the same uncertainty, which is a requirement for the statistical test you're using. And they certainly don't have the uncertainty you imply by taking the standard deviation: The figure for Bosnia is much, much more likely to be accurate than the figures for Kosova and Croatia, if for no other reason than the fact that the numbers involved are an order of magnitude bigger.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 16th, 2009 at 08:37:22 AM EST
[ Parent ]
Because of their relative size? Because they were precisely different wars? Why? In that case, none of the 8 points involved have the same uncertainly level.

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.

by vladimir on Mon Mar 16th, 2009 at 08:48:15 AM EST
[ Parent ]
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.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 16th, 2009 at 09:32:03 AM EST
[ Parent ]
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?

by vladimir on Mon Mar 16th, 2009 at 09:38:39 AM EST
[ Parent ]
I would use weighted averages, as I said above. You can play with them in different ways to get different kinds of information, but as long as we don't have any really good ways to estimate uncertainties, there is no way you'll ever get a "significance test" in the ordinary sense of the term.

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.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 16th, 2009 at 09:43:06 AM EST
[ Parent ]
What exactly is your null hypothesis?

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 09:44:41 AM EST
[ Parent ]
That Serbs are more likely to be indicted/sentenced than non Serbs - one tailed.
by vladimir on Mon Mar 16th, 2009 at 09:57:48 AM EST
[ Parent ]
That is not a null hypothesis. The null hypothesis is an unbiased court.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 09:59:35 AM EST
[ Parent ]
It can be for a t test which can be used to check for a statistically significant difference between the means of two samples.
by vladimir on Mon Mar 16th, 2009 at 11:32:06 AM EST
[ Parent ]
In that case the null hypothesis is the equality of means - that is, lack of bias.

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

by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 12:00:58 PM EST
[ Parent ]
Correct and that's why I calculated the variance of the 2 different data sets.
by vladimir on Mon Mar 16th, 2009 at 12:05:53 PM EST
[ Parent ]
What parameter are you trying to estimate again?

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 12:07:43 PM EST
[ Parent ]
A t test is specific for small sample populations. Why use Poisson?
by vladimir on Mon Mar 16th, 2009 at 11:39:21 AM EST
[ Parent ]
A t test is specific for Gaussian variables.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 11:58:49 AM EST
[ Parent ]
And why do you assume that the number of indicted or convicted war criminals per number of civilian casualties follow a Gaussian distribution?
by vladimir on Mon Mar 16th, 2009 at 12:04:07 PM EST
[ Parent ]
I don't, that's why I haven't said you should use a t-test.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 12:08:23 PM EST
[ Parent ]
You could say the number of indicted or convicted war criminals is a Poisson distribution with parameter proportional to the number of civilian casualties, and estimate the coefficient of proportionality.

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

by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 12:16:15 PM EST
[ Parent ]
What is the size of the relevant population?

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

by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 10:02:57 AM EST
[ Parent ]
By which I mean, in an unbiased court, what would you expect the number of indictments to be proportional to? We have had a large number of incompatible measures thrown about for days.

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

by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 09:58:56 AM EST
[ Parent ]
So it's Poisson we should be using.
by vladimir on Mon Mar 16th, 2009 at 10:06:30 AM EST
[ Parent ]
Yes, but you need a sensible null hypothesis for the behaviour of an unbiased court.

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

by Migeru (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 10:07:50 AM EST
[ Parent ]
That's quite intuitive, I guess. I for one payed nearly no attention on the two micro wars.

Free at last! Free at last! Thank God Almighty, we are free at last! (Martin Luther King)
by ValentinD (walentijn arobase free spot franša) on Mon Mar 16th, 2009 at 03:16:52 PM EST
[ Parent ]

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