A Statistical Analysis of the ICTY's bias. | 220 comments (213 topical, 7 editorial, 0 hidden)

Re: A Statistical Analysis of the ICTY's bias. (none / 1)

By comparing the ratio of the Serb mean of Indicted versus enemy civilian casualties to the other group (Bosnians, Albanians, Tutsis, Germans and Croats) we see that we have 5,13 more Serbs convicted per enemy civilian casualty than the other groups.

No you don't. To find the ratio of indicted Serbs to other people's civvies, you need to do a weighted average, but you're doing a vanilla average.

When you do a weighted average, you get 2.16 indicted Serb for every 1000 enemy civilians, and 2.16 indicted Croat or Bosniac for every Serb civilian. And you get 1.02 convicted Serb for every 1000 enemy civilians, while you get 0.89 Bosniac and Croat convictions for every 1000 Serb civilians.

Also do note that the ratio of convictions will likely change as time progresses, because there is a number of indictees whose trials are not yet finished (that's a story in and of itself, but let's save that for another day).

The figures for Rwanda and Nürnberg are of somewhat dubious value to this discussion: The way you are using it assumes a linear relationship between the number of civilian deaths and the number of war criminals - that's a pretty reasonable assumption when we're talking about wars in the same ballpark (in this case between a couple of thousand civilian deaths and a couple of tens of thousands). But it may or may not be reasonable to extend it to wars involving hundreds or millions of civilian casualties.

(And of course, Re: Nürnberg, one should not forget that the Russians shot a couple of thousand Nazis in the DDR for war crimes and other stuff...)

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Sun Mar 15th, 2009 at 05:57:29 PM EST

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

What do you mean by weighted average, how do you weigh it?
And do you mean 2.16 indicted Serb for every 1000 civilians - or civilian war casualties ?

Free at last! Free at last! Thank God Almighty, we are free at last! (Martin Luther King)

by ValentinD (walentijn arobase free spot frança) on Sun Mar 15th, 2009 at 06:26:27 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

Civilian casualties, as that is what the subject deals with. (One could also divide by the number of displaced people, or the number of permanently displaced people, but right now, we're dealing with civilian casualties during the war.)

Weighted average. In this case weighted by the number of civilian deaths that went into each individual ratio.

The weighted average is preferable because the lower numbers of necessity have higher uncertainties associated with them - similar to the batting averages in the first example here

For the same reasons, the standard deviations given in the diary are nonsense, and cannot be used to show significance.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Sun Mar 15th, 2009 at 06:37:21 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 1)

Call me a statistical dilletant, I still can't see how using weighted averages in this example would change anything - I don't see how you got your numbers either, btw. Are you speaking about the averages made with the numbers of the three wars?

To me he sounds like trying to say that serb casualties are bigger and so are serb indictions and convictions.

Now I would understand if you protested the principle of this thread, that the number of casualties should be (directly or not) related to the number of indicted, which to me is not quite so obvious.

Anyway, the fact that the West declared the Serbs to be the Enemy is in itself sufficient proof that the "international court" established by the West amongst themselves (as usual) is biased. We can't seriously expect the albanian leaders who allowed their people to be butchered indicted, or a dutch judge to declare US or Germany as the instigators of this conflict. Just as we can't expect Bush brought to justice for going to war in Iraq without a UN Sec. Council resolution, and without any proof at all. Duh.

Free at last! Free at last! Thank God Almighty, we are free at last! (Martin Luther King)

by ValentinD (walentijn arobase free spot frança) on Sun Mar 15th, 2009 at 07:40:10 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

OK, I should have been clearer about where my figures come from.

I simply take the total number of Serbian indictees (15+71+13 = 99) and divide by the total number of non-Serb civilian casualties from wars they were involved in (3368+38000+4500 = 45868). And then I do the same for (Croats+Bosniacs) - while remembering that they didn't have any hand in the Serbian casualties in Kosova, on account of them not being in Kosova during the war there.

That gives you the numbers I cite in the top-level comment.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 16th, 2009 at 05:41:40 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

You're saying that for the Serb data, I should calculate as if it were 1 war and not 3 separate wars. It's certainly not 1 war. It could eventually be 2 wars.

If I choose to calculate as 3 separate wars, with 3 specific data points, I'm not contravening any statistical rules and I have a case from a historical perspective. So my hypothesis holds.

by vladimir on Mon Mar 16th, 2009 at 08:22:11 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

sigh

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

What exactly is your null hypothesis?

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith

by Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 09:44:41 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 09:59:35 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 12:00:58 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 12:07:43 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 11:58:49 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 12:08:23 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 12:16:15 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 10:02:57 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 09:58:56 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

So it's Poisson we should be using.

by vladimir on Mon Mar 16th, 2009 at 10:06:30 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 10:07:50 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

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 frança) on Mon Mar 16th, 2009 at 03:16:52 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

You're right - I overlooked that. But the proof of bias is there... whether you use a weighted average or vanilla average.

by vladimir on Mon Mar 16th, 2009 at 03:57:19 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

You call a 1:1 correspondence in indictments a proof of bias? A 10:9 correspondence in convictions? There is a possible bias in favour of Albanians, but that does not mean that there is a bias against Serbs.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 16th, 2009 at 05:20:28 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

Then we're not comparing the same thing. You said that the group's average should be weighted... and indeed that can be an approach - which would change the estimated factor of bias - but it wouldn't change the t test results - which confirm that there is a statistically significant difference between the two groups being compared.

By weighing the group's average, you don't change any individual ethnic group's results. If you look at these results (in the last graph provided in the diary), you'll see that in the Bosnian war, it appears that all ethnic groups are treated equally. However, these figures work on the wrong assumption that there was no killing of Croats by Muslims and vice-versa...

Compared to Muslims & Croats in Bosnia we have:
> a bias of 100:135 against Serbs in Croatia
> a bias of 100:179 against Serbs in Kosovo
> a bias of 22:100 in favour of Albanians
> a bias of 0:100 in favour of Croatian Croats

by vladimir on Mon Mar 16th, 2009 at 05:44:01 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 1)

No, I'm saying that all your averages and standard deviations should be weighted by the denominators that went into your ratios.

And your comparisons of conviction rates are pure, mean-spirited garbage, because there are still cases outstanding which will in all probability change most of those figures significantly. Compare indictments, or break down the indictments into convictions, acquittals and outstanding cases, if you like to. But using only convictions is nonsense as long as there are cases outstanding.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 16th, 2009 at 05:55:23 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 1)

Bull shit Jake. That's something you could eventually argue had the tribunal been set up last year. But after 16 years of the tribunal's work, taking the convictions is perfectly legitimate. Look at Seselj, he's been in jail for 6 years, with no exit date in view... and is without a conviction and even without a trial (it's been indefinitely adjourned)! Where would you put him?

It's perfectly plausible to say that the outstanding cases will follow the same pattern as those already finished. Unless you have some inside information that there is an army of Croats and Albanians in the dock waiting to be convicted.

by vladimir on Mon Mar 16th, 2009 at 06:14:52 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

vladimir:

Unless you have some inside information that there is an army of Croats and Albanians in the dock waiting to be convicted.

Bull shit vladimir, by your own data there are 6 Croats whose trial is "ongoing" (and 2 have been transferred to national courts) vs. 9 (+8) Serbs. So there are proportionally more Croatian cases outstanding than Serb.

Regarding Kosovo, it is a well-known fact that when the number of people in a category drops below about 5, statistical tests become insufficiently powerful. In the case of Kosovo the expected numbers are small enough you can't really draw any conclusions.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith

by Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 06:23:09 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

Bull shit migeru ;)

That's a ratio of 8 Croats : 17 Serbs.
Croatian population= 4,5 M
Serbian population= 8 M (not counting Kosovo Albanians)

by vladimir on Mon Mar 16th, 2009 at 06:44:52 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 1)

it looks even

by vladimir on Mon Mar 16th, 2009 at 06:45:34 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

You don't compare to the population, you compare to the number of indictments in which the ratio is closer to 3:1 than to 2:1.

You are beginning to appear disingenuous. You keep moving the goalposts.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith

by Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 06:47:59 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

My fault.

by vladimir on Mon Mar 16th, 2009 at 06:54:08 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

But even with 3:1... we're in the same ball park. It's not going to change your end result by very much.

by vladimir on Mon Mar 16th, 2009 at 06:55:16 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

Look, I'll be the first to argue that keeping people locked up for decades without trial is a monstrous travesty of justice. I'd argue that Adolf fucking Hitler should be released if you couldn't convict him after five years. But there are a couple of points here that you fail to account for:

Not all the cases started at the same time, because some of the indictees were better at evading capture than others.
You can reasonably expect (at least to first order) that the ratio between convictions and acquittals hold up - so you could use the figure [convictions*(1 + ongoing/acquittals)] if you wanted to. But using just convictions remains nonsense.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 16th, 2009 at 06:26:19 AM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

You know, you really shouldn't be making even an implicit comparison between Seselj and Hitler.

by vladimir on Mon Mar 16th, 2009 at 01:25:08 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

Actually, even better than convicted, we could use the severity of the conviction (number of years sentenced to prison). But that's also something that would take time to compile. Really, all the other indicators can be politically charged - including for example, convicted and then released 1 year later.

The cases outstanding only favour the Croats and this by a very small margin. So I'd still go with the convicted indicator.

by vladimir on Mon Mar 16th, 2009 at 01:41:27 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

Remember that the more variables you throw into your model the least significant are the results.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith

by Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 01:47:18 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

vladimir:

The cases outstanding only favour the Croats and this by a very small margin. So I'd still go with the convicted indicator.

Are you cherry-picking your indicators?

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith

by Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 01:48:52 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

Why are you insinuating that? I'm just reacting to Jake's comment about me being mean spirited (which I really didn't appreciate) and explaining why I think the convicted indicator is best.

by vladimir on Mon Mar 16th, 2009 at 01:51:23 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

My being mean spirited because I chose the 'convicted' indicator and not the 'acquitted indicator' which in his opinion was much better.

by vladimir on Mon Mar 16th, 2009 at 01:52:40 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

You misunderstand the use of "mean-spirited". Focus on this instead

Compare indictments, or break down the indictments into convictions, acquittals and outstanding cases, if you like to. But using only convictions is nonsense as long as there are cases outstanding.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith

by Carrie (migeru at eurotrib dot com) on Mon Mar 16th, 2009 at 01:55:43 PM EST
[ Parent ]

Re: A Statistical Analysis of the ICTY's bias. (none / 0)

First, it's the comparison that I call mean spirited, not you - apologies if that wasn't clear.

Second, I'm not arguing that you should use acquittals - I'm arguing that you should use [convictions*(1 + ongoing/acquittals)], which, unlike convictions, would make sense... kind of.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 16th, 2009 at 02:00:40 PM EST
[ Parent ]

A Statistical Analysis of the ICTY's bias. | 220 comments (213 topical, 7 editorial, 0 hidden)

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