statistics question

[gmann]

Re: statistics question

Thanks. There are pieces of my brain all over the keyboard.

[unofan]

Re: statistics question

It may well be the case that there is a key data element missing here. Your question is framed assuming the allocation of jurors is pretty much done by random chance.

However, juries are not completely chosen at random because the attorneys for each side often can challenge whether a particular juror is seated or not. Sometimes they can challenge "for cause" based on answers to questions; sometimes they have a "peremptory challenge" (limited in number) by which they can reject someone with no reason.

In other words, one of the attorneys may have skewed the jury pool during the jury selection process.

Now, perhaps that is what you are trying to establish?? even so, wouldn't potential supporting evidence also be available from which potential jurors were dismissed during the formation of the jury? if you had that evidence, couldn't you then see how many people dismissed via "peremptory challenge" had characteristic A relative to other people who were dismissed?

Oh, the final jury itself was certainly skewed intentionally. Characteristic A is not a legally protected characteristic and the county attorney could (and did) legally strike all 4 people with characteristic A using his pre-empts.

The main question I wanted to know is how unlucky was it to have no more than 4 out of 20 people (since each attorney only has 4 strikes and there's no way my wife would have not kept at least one person with characteristic A on the final jury if she had the choice) with characteristic A on the panel, when the overall population has that at ~70% clip. My wife (and her client) will be thrilled to know it was literally a 1-in-a-million shot.

[LynahFan]

Re: statistics question

It may well be the case that there is a key data element missing here. Your question is framed assuming the allocation of jurors is pretty much done by random chance.

However, juries are not completely chosen at random because the attorneys for each side often can challenge whether a particular juror is seated or not. Sometimes they can challenge "for cause" based on answers to questions; sometimes they have a "peremptory challenge" (limited in number) by which they can reject someone with no reason.

In other words, one of the attorneys may have skewed the jury pool during the jury selection process.

Now, perhaps that is what you are trying to establish?? even so, wouldn't potential supporting evidence also be available from which potential jurors were dismissed during the formation of the jury? if you had that evidence, couldn't you then see how many people dismissed via "peremptory challenge" had characteristic A relative to other people who were dismissed?

Well, of course - jury selection is definitely not random (read some John Grisham!). But when the question is posed as "how unlucky was I?" the implication is to figure out the probability as if luck really were the only factor.

I transcribed my earlier results incorrectly - I'll edit to fix.

The overall probability for getting a jury with 0 yeses from a panel of 20 where the overall population is 70% yes turns out to be 5.e-7, or 1 in 1.89 million.

[FreshFish]

Re: statistics question

It may well be the case that there is a key data element missing here. Your question is framed assuming the allocation of jurors is pretty much done by random chance.

However, juries are not completely chosen at random because the attorneys for each side often can challenge whether a particular juror is seated or not. Sometimes they can challenge "for cause" based on answers to questions; sometimes they have a "peremptory challenge" (limited in number) by which they can reject someone with no reason.

In other words, one of the attorneys may have skewed the jury pool during the jury selection process.

Now, perhaps that is what you are trying to establish?? even so, wouldn't potential supporting evidence also be available from which potential jurors were dismissed during the formation of the jury? if you had that evidence, couldn't you then see how many people dismissed via "peremptory challenge" had characteristic A relative to other people who were dismissed?

[LynahFan]

Re: statistics question

Given the panel of 16 "nos" and 4 "yeses" you can calculate the probability of getting none on the jury pretty easily. The probability that the first pick is a no is 16/20, the second would be 15/19, etc. These are each independent "events", so you just multiply the 12 probabilities together 16/20*15/19*14/18....*5/9 = 0.014. So there's only a 1.4% chance of drawing a jury with zero "nos" from a panel with 16/20 "yeses."

To get the panel in the first place, you're best off using the Binomial distribution. To get exactly 4 "successes" (k) in 20 trials (n) where the population is 70% yes (p) would be:

P = 20!/(16! * 4!) * .7^4 * (1-.7)^(20-4) = (20*19*18*17)/(4*3*2) * .24 * 4.3e-9 = 4845 * 1.03e-9 = 0.000005

Therefore, the total probability of getting that jury from that pool from the overall population = .014*.000005 = 7.23e-8, i.e. there's only a "1 in 13.8 million" chance of it happening if all the events are random.

However, the overall probability of getting zero yeses on your jury is actually quite a lot better than that, because there are 9 possible jury pools which could yield a jury with zero yeses (any pool with between 0 and 8 yeses). I have to run to work now, but I'll write a script when I get there.

[unofan]

Just curious if any statistics guru out there can tell me just how bad my wife's jury pool was this afternoon. I used to be able to do this stuff back in college but cant remember how at this point.

persons on panel: 20
persons on panel with characteristic A: 4
Persons on the final 12-person jury with characteristic A: 0
Average percentage of population with characteristic A: 70%
# of registered voters: 64,000

Needless to say, her client was found guilty. Can anyone tell me just how unlucky of a panel/jury she got?