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You can also simplify.
  • calculate the ratio of convicted (or indicted) per civilian casualties for each war / ethnic group
  • do a test to identify whether the differences between the means of these ratios is statistically significant from one group to another.
If it is, you probably have a biased court. If it's not, you probably don't have a biased court.
I used the t test because its appropriate for small data samples in a normal (Gaussian) distribution, which is an assumption that seems ok to me.
by vladimir on Tue Mar 17th, 2009 at 06:19:17 AM EST
[ Parent ]
Do this. From

plot Indicted vs. Casualties on a log-log plot. Can you actually see the diference?

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 Tue Mar 17th, 2009 at 06:24:06 AM EST
[ Parent ]
Gotta run. Will be busy until tomorrow morning...
by vladimir on Tue Mar 17th, 2009 at 06:30:28 AM EST
[ Parent ]
So, here's the chart.

The triangles are the cases where the Serbs are the civilians and the circles the cases where the Serbs are the indictees. The two points nearest the upper right are the war in Bosnia.

And here's the fit to all six points together (that's the null hypothesis):
Coefficients:
    (Intercept)  log(casualties)  
    -4.0792       0.7741  

Response: log(indicted)
        Df Sum Sq Mean Sq F value  Pr(>F)  
log(casualties)  1 3.3419  3.3419  13.880 0.02038 *
Residuals     4 0.9631  0.2408         
 


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 Tue Mar 17th, 2009 at 04:02:50 PM EST
[ Parent ]
So only two of the data points fall any distance away from the line, and are the data sets sufficiently large for that to mean anything significant?

Any idiot can face a crisis - it's day to day living that wears you out.
by ceebs (ceebs (at) eurotrib (dot) com) on Tue Mar 17th, 2009 at 04:11:41 PM EST
[ Parent ]
The one clear outlier corresponds to Albanian indictees and Serb civilians.

With only 6 points it is really difficult to argue anything. For instance, what is the chance that all three "Serb indictee" points are above the line? 1 in 8. This is not sufficient to show bias at 90% confidence (you would need the probability to be less than 1 in 10) let alone 95% confidence (1 in 20).

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 Tue Mar 17th, 2009 at 04:17:48 PM EST
[ Parent ]
However, that might be the result of a difference in data sources:
Most of the civilian casualty figures were obtained from Wikipedia - which itself uses the ICTY, the Red Cross and for the Serbian civilian casualty figures in Kosovo, an EU funded project run out of Belgrade.
From wikipedia
According to a Serbian government report, from January 1, 1998 to June 10, 1999 the KLA killed 988[5] people and kidnapped 287[5]; in the period from June 10, 1999, to November 11, 2001, when NATO had been in control in Kosovo, 847[5] people were reported to have been killed and 1,154[5] kidnapped. This comprised both civilians and security forces personnel: of those killed in the first period, 335[5] were civilians, 351 were soldiers, 230 were police and 72 were unidentified; by nationality, 87 of killed civilians were Serbs, 230 Albanians, and 18 of other nationalities.[5] The Humanitarian Law Center in Belgrade, an organization funded by the European Commission, have announced that it had identified 8,000 Serbians out of a total of 12,000 casualties they had identified in the Kosovo War. [53]


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 Tue Mar 17th, 2009 at 04:22:34 PM EST
[ Parent ]
co-incedentally Looking at the Wikipedia article on the Iraq war, it is noticeable that all the War crimes examples in there are not American. So the people prosecuted for Abu-Ghraib are not in the list of indictees even though their activities should be considered so under the Geneva conventions.

Any idiot can face a crisis - it's day to day living that wears you out.
by ceebs (ceebs (at) eurotrib (dot) com) on Tue Mar 17th, 2009 at 04:50:38 PM EST
[ Parent ]
No, because - as we went over at considerable length in the thread above - a t-test with Gaussian uncertainties requires that the uncertainties are uniform, which they manifestly are not.

If you must insist on treating these three points as independent - which I can see little justification for doing, but maybe that's just me - you do a (casualties, indictments, convictions) plot and run a linear fit against all three points in a given series at the same time. This way you get some more meaningful (implicit) assumptions about the way the uncertainties look.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Tue Mar 17th, 2009 at 07:54:52 AM EST
[ Parent ]
The sensible thing to do is a fit in a log-log plot - the "intercept" is the quantity of interest here, and the "slope" is being taken as 1 but could be fitted too.

Or, rather, three fits.

One for all six rows in Vladimir's table - that's the "null hypothesis".

One for the 3 Serb rows and the 3 non-serb rows. That's more or less equivalent to was was done in the diary.

Or you could do a test on whether the 3 Serb and 3 non-Serb points fall above or below the "null hypothesis" regression line. The trouble is, with only 6 points you probably can't say anything with 95% confidence.

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 Tue Mar 17th, 2009 at 08:06:03 AM EST
[ Parent ]
AFAICT, that's substantially the same thing I'm doing below.

I would be opposed to fitting the slope as well as the intercept in your model, because we already only have three points for every fit parameter - and you fit a number of parameters comparable to your number of data points at the peril of talking nonsense...

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Tue Mar 17th, 2009 at 09:05:43 AM EST
[ Parent ]
This is what happens when you set the slope to 1 and only fit the intercept:

This actually makes it look worse for Vladimir's hypothesis.
The fit is this:

Coefficients:
(Intercept)  
     -6.095  

Response: log(indicted) - log(casualties)
	  Df  Sum Sq Mean Sq F value Pr(>F)
Residuals  5 1.24772 0.24954  


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 Wed Mar 18th, 2009 at 03:01:38 AM EST
[ Parent ]
vladimir:
I used the t test because its appropriate for small data samples in a normal (Gaussian) distribution, which is an assumption that seems ok to me.
It is not ok because a ratio is generally not distributed as 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 Tue Mar 17th, 2009 at 09:31:06 AM EST
[ Parent ]

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