The U.S. has bilateral extradition treaties with many...

The U.S. has bilateral extradition treaties with many countries. (A person charged with a crime in his home country may escape to the U.S.: if he is captured in the U.S., authonties in his home country may request that he be"extradited," that is, turned over for prosecution under their laws.) The Senate attached a special rider to the treaty governing extradition to Northern Ireland: fugitives cannot be retumed if they will be discriminated against on the basis of religion. In a leading case, the defense tried to establish discrimination in Northern Ireland's criminal justice system. One argument was based on 1991 acquital rates for persons charged with terrorist offenses. $^{17}$ According to a defense expert, these rates were significantly different for Protestants and Catholics: $\chi^{2} \approx 6.2$ on 1 degree of freedom, $P \approx 1 \% .$ The data are shown below: 8 Protestants out of 15 were acquitted, compared to 27 Catholics out of $65 .$ (a) Is the calculation of $x^{2}$ correct? If not, can you guess what the mistake was? (That might be quite difficult.) (b) What box model did the defense have in mind? Comment brieffy on the model.

The U.S. has bilateral extradition treaties with many countries. (A person charged with a crime in his home country may escape to the U.S.: if he is captured in the U.S., authonties in his home country may request that he be"extradited," that is, turned over for prosecution under their laws.)
The Senate attached a special rider to the treaty governing extradition to Northern Ireland: fugitives cannot be retumed if they will be discriminated against on the basis of religion. In a leading case, the defense tried to establish discrimination in Northern Ireland's criminal justice system.
One argument was based on 1991 acquital rates for persons charged with terrorist offenses. $^{17}$ According to a defense expert, these rates were significantly
different for Protestants and Catholics: $\chi^{2} \approx 6.2$ on 1 degree of freedom,
$P \approx 1 \% .$ The data are shown below: 8 Protestants out of 15 were acquitted,
compared to 27 Catholics out of $65 .$
(a) Is the calculation of $x^{2}$ correct? If not, can you guess what the mistake
was? (That might be quite difficult.)
(b) What box model did the defense have in mind? Comment brieffy on
the model.

Key Concepts

P-Value and Statistical Significance

The p-value is a measure used in hypothesis testing to indicate the probability of observing data as extreme as, or more extreme than, the current set under the null hypothesis. It helps determine whether the observed effect, such as a difference in group outcomes, is likely to be real or if it could have occurred by random chance, thereby guiding conclusions about discrimination or other effects.

Box Model in Randomization

The box model is a conceptual framework often used in statistics to represent a population of elements from which samples are drawn randomly. In the context of hypothesis testing, it helps illustrate the process of random chance influencing outcomes, by simulating draws from a box of outcomes to see if the observed distribution of events is consistent with random variation under the null hypothesis.

Degrees of Freedom

Degrees of freedom in statistical tests, such as the chi-square test, refer to the number of independent values or quantities that can vary in the analysis without breaking any constraints. In a typical 2x2 contingency table, degrees of freedom are calculated as (number of rows - 1) multiplied by (number of columns - 1), which, in many simple cases, results in one.

Chi-Square Test for Categorical Data

The chi-square test is a statistical method used to analyze categorical data by comparing observed frequencies with expected frequencies under a null hypothesis. In legal and forensic contexts, this test can be used to investigate whether differences in outcomes, such as acquittal rates among different groups, are statistically significant or simply due to chance.

Legal Safeguards Against Discrimination

Many treaties include provisions that prevent the extradition of fugitives who might face discriminatory treatment in the requesting country. This concept encapsulates the idea that legal processes, including extradition, should operate without bias based on characteristics such as religion, ensuring fairness and the protection of individual rights under international law.

Bilateral Extradition Treaties

These are international legal agreements between two countries that establish the conditions and procedures for surrendering individuals charged with criminal offenses. They often contain clauses that address concerns like discrimination or human rights, ensuring that extradition is conducted fairly in accordance with both nations' laws.

Transcript

00:01 So here in this question, the data are provided concerning the outcomes of 80 trials in a country divided on lines of religion.

00:10 And the chart of court decisions and religion is given to us.

00:12 So i'm going to just redraw the chart here.

00:16 So here we have the acquitted and then we have the convicted values.

00:25 All right.

00:25 And this is for the protestant.

00:30 And we have catholic.

00:34 So i'm going to find out the totals for all the values.

00:36 That we've been given.

00:39 All right and okay so now the data that is given to us is over here we have eight and then seven so this is 27 and then 38 now at the total of this horizontal total would be 35 then this is 45 so if you add them you get the total here as 80 and similarly vertical totals here this is 15 and this is 65 so in this way the addition is 80 now we are supposed to test the hypothesis that the trial outcome is independent of religious affiliation.

01:25 So we're going to do this by a kai square test for independence.

01:29 Now we're supposed to find out the expected, like these are the observed frequencies and values that we've figured out.

01:34 But we are supposed to find out the expected values also.

01:40 So the table for the expected values, i'm going to make it here again.

01:49 Okay, so we're going to again copy down the same things that we have.

01:57 So here is the protestant and then the catholic, then the total, and then we have three rows again.

02:09 One is for the acquitted and then the convicted and then the total.

02:21 Now to find out the values for the expectations over here, the formula or the logic that we will be applying to simplify this part is you can see that over here the horizontal total.

02:43 If i'm going to calculate the value for the equated protestants like this value, i'm going to consider the total of the protestant over here, which is 15, and then the total over here which is 35.

02:54 So i'm going to highlight this.

02:56 To calculate this value, okay, i'm going to take 15 into 35 and then divide by the total 80.

03:06 So it's going to give me a value here.

03:08 So i'm going to write this over here.

03:10 This is actually going to be 15 into 35 upon 80 okay and if you simplify then the value you're going to get here is 6 .56 so in a similar way over here we're going to consider 65 into 35 upon 80 so then this value is going to be 28 .44 now you consider these values such that you always know the total is going to remain the same so this will be 35 45 80 as it is over here also this is supposed to be 15 and 65 as it is so if you do not want to calculate them in this way now since you know the first values you can always do 15 minus 6 .56 so i'm doing that 15 minus 6 .56 so this will be giving me the value as 8 .44 and similarly over here when i do 65 minus 28 .44 so this is going to give me the value as 36 .56.

04:20 Now i am done with finding the expected values out here so now based on this we are supposed to find out the kai square for the data that we have.

04:30 So i'm going to formulate a new table again...

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