statistics question

[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?

 

[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 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.

 

[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

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.

 

[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.

 

[gmann]

Re: statistics question

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

 

[leswp1]

Re: statistics question

no math My brain froze. Safer than falling all over the keyboard.

 

[gopheritall]

Re: statistics question

Those darn left handed people always stick together!

 

[LynahFan]

Re: statistics question

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.

Well, don't be so sure. The jury panel isn't really a random sample, either. First of all, their names have to be on a list (registered voters, licensed drivers, etc) which is automatically self-selecting, then they have to be the people who didn't have a compelling reason to get out of it (all manner of people are exempt from jury duty), etc. It would never pass muster with a statistician as a random sample.

 

[UncleRay]

Re: statistics question

"A jury of one's peers" is what comes to mind.

 

[unofan]

Re: statistics question

Those darn left handed people always stick together!

Good guess, but no.

Well, don't be so sure. The jury panel isn't really a random sample, either. First of all, their names have to be on a list (registered voters, licensed drivers, etc) which is automatically self-selecting, then they have to be the people who didn't have a compelling reason to get out of it (all manner of people are exempt from jury duty), etc. It would never pass muster with a statistician as a random sample.

Let's just say there's nothing inherent about Characteristic A that would, on its face, be more likely or less likely to appear on the juror lists than the population at large. Also, if anything, it would've been more likely to appear in this county than in the nation as a whole, given the town that constitutes the bulk of the population for the county.

And we dont need to worry about strikes for cause, either, since the judge didn't allow any. The original panel of 20 was made up of the first 20 jurors off the randomized list.

 

[FlagDUDE08]

Re: statistics question

Those darn left handed people always stick together!

Dang straight we do! We're in our right minds.

 

[Kepler]

Re: statistics question

Those darn left handed people always stick together!

No, our problem is we're all mutually orthogonal in infinite directions!

For the record, my guess for characteristic A is "college educated."

As was mentioned, the key is to apply binomial probability.

If 70% of the population is A, then the probability of *no more than* 4 out of 20 from a random sample (the panel) being A equals:

P(X <= 4) where the probability is given at the prior link.

Here is a binomial calculator. Entering the values: .7, 20, 4 and clicking Calculate gives P (X <= 4) of 5.55 E-06 or .00000555, or roughly 180,000 to 1.

Since the panel was a blind selection from the population, that is really, really, really unlucky.

 

[pirate]

"A jury of one's peers" is what comes to mind.

This pool would be created after people had acknowledged the 'invite' correct? Those with valid reasons to skip attending, which consists of just taking the time to write in where I live, will not be in the pool. Those May be a distinct type of person, likely employed, likely professional etc, could also exclude single parents etc

 

[Patman]

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 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.

Careful... its common accepted practice in these situations to look at the entire tail... afterall, if i had a 500 person panel any result will be very rare.

That being said, i would think the eye-ball situation seems about right... but you also have to remember that people actually show up for jury duty and they don't always hunt you down if you don't show. Also you have to consider that odd situations do occur in the stream of reality... while your wife is a one-shot deal if this is over months and years something weird has a higher chance than you think. Like for example, the chance of 3 perfect games in a single month is not nearly as remote as one may want to believe.

edit: ok, its more like 1 in 180,000 for a single instance... and over the course of a work year the chance of it happening is still small 1 in 721... I'd still wonder about self-selection... no shows.

 

[LynahFan]

Re: statistics question

Careful... its common accepted practice in these situations to look at the entire tail... afterall, if i had a 500 person panel any result will be very rare.

Right - that's why I said you should really consider all 9 possible panels that could result in zero As on the jury.

That being said, i would think the eye-ball situation seems about right... but you also have to remember that people actually show up for jury duty and they don't always hunt you down if you don't show. Also you have to consider that odd situations do occur in the stream of reality... while your wife is a one-shot deal if this is over months and years something weird has a higher chance than you think. Like for example, the chance of 3 perfect games in a single month is not nearly as remote as one may want to believe.

Yes - lots of self-selection involved in juries.

edit: ok, its more like 1 in 180,000 for a single instance... and over the course of a work year the chance of it happening is still small 1 in 721... I'd still wonder about self-selection... no shows.

1 in 180000 for the panel to contain 4 or fewer As, but it would still be considerably less likely than that (by orders of magnitude) for the actual jury to contain zero As.

I think only about 40% of Americans have 4-year or 2-year college degrees, so it's more likely that 70% = people without a 4-year degree.

 

[Kepler]

Re: statistics question

1 in 180000 for the panel to contain 4 or fewer As,

Which was his question.

I think only about 40% of Americans have 4-year or 2-year college degrees, so it's more likely that 70% = people without a 4-year degree.

Which was what would make it interesting. Figure a college town, so tons of people with at least some college on their record. The 1:180k draw is statistically unlucky; then whichever lawyer has the weaker case gets rid of the 4 remaining possibilities for, I dunno, poor hygiene (entirely believable), which was not unlucky in the least, but that's beside the point.

We were just having fun guessing, anyway. Everybody knows the real answer is "lesbians," and the county is Grafton Cty, NH.

 

[Patman]

Re: statistics question

Right - that's why I said you should really consider all 9 possible panels that could result in zero As on the jury.


Yes - lots of self-selection involved in juries.

1 in 180000 for the panel to contain 4 or fewer As, but it would still be considerably less likely than that (by orders of magnitude) for the actual jury to contain zero As.

I think only about 40% of Americans have 4-year or 2-year college degrees, so it's more likely that 70% = people without a 4-year degree.

Yes, but lawyers are allowed to discriminate in dismissing jurors pre-trial (laws of the state may vary, etc, etc.)... rightly or wrongly. The only true question of a rigged pool is in situations where the pool isn't supposed to be rigged. How many 18 year-olds sit on drunk driving juries? Its a different thing if your black box isn't really a black box... that's a problem... but the final jury can be a matter of juror characteristics and thus the metric of "fair" becomes arbitrary.

The last case, would be a hypergeometic distribution if you believed that assignments should be random... that being said, in light of the above, we are very sure they aren't random.

edit: I should point out that i found the chance of a 20 person pool having 4 people (or fewer) with that characteristic. The final question can be skinned as a probability question but only if you assume there is supposed to be a truly random equal probability metric... our knowledge of the courts say there isn't.

 

[unofan]

Re: statistics question

Right - that's why I said you should really consider all 9 possible panels that could result in zero As on the jury.

Except in the hypothetical case where there are only five-8 A's on the panel, my wife would have made sure at least one of them stayed on. The only way to get 0 on the final jury in this scenario is if the county attorney could strike them all, which means 4 or fewer, not 8 or fewer.

And Patman, intentionally or not, guessed 'A.' The charge was OWI 1st, and the panel only had four people who had even touched alcohol in their lives. The other 16 were prohibitionists. In a freaking college town.

 

[Patman]

Except in the hypothetical case where there are only five-8 A's on the panel, my wife would have made sure at least one of them stayed on. The only way to get 0 on the final jury in this scenario is if the county attorney could strike them all, which means 4 or fewer, not 8 or fewer.

And Patman, intentionally or not, guessed 'A.' The charge was OWI 1st, and the panel only had four people who had even touched alcohol in their lives. The other 16 were prohibitionists. In a freaking college town.

It also helps that I've been through the jury pool cycle and I saw a couple of drunk driving case where they gave a boot to anybody who looked young... Including myself as I drew a low number and was 20 at the time.

I'd also say that I figured this would be a race thing.