Announcement

Collapse
No announcement yet.

statistics question

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • statistics question

    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?

  • #2
    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.
    Last edited by LynahFan; 02-29-2012, 09:48 AM.
    If you don't change the world today, how can it be any better tomorrow?

    Comment


    • #3
      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?
      Last edited by FreshFish; 02-29-2012, 08:53 AM.
      "Hope is a good thing; maybe the best of things."

      "Beer is a sign that God loves us and wants us to be happy." -- Benjamin Franklin

      "Being Irish, he had an abiding sense of tragedy, which sustained him through temporary periods of joy." -- W. B. Yeats

      "People generally are most impatient with those flaws in others about which they are most ashamed of in themselves." - folk wisdom

      Comment


      • #4
        Re: statistics question

        Originally posted by FreshFish View Post
        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.
        If you don't change the world today, how can it be any better tomorrow?

        Comment


        • #5
          Re: statistics question

          Originally posted by FreshFish View Post
          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.
          Last edited by unofan; 02-29-2012, 06:36 PM.

          Comment


          • #6
            Re: statistics question

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


            Comment


            • #7
              Re: statistics question

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

              Comment


              • #8
                Re: statistics question

                Those darn left handed people always stick together!
                Bottom Line: If you deserve to win the national championship then don't worry about who you play, when, and where. Just keep winning.
                Exception: You are right about the refs. They, no doubt, have it in for <insert your team name here>!

                Comment


                • #9
                  Re: statistics question

                  Originally posted by unofan View Post
                  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.
                  If you don't change the world today, how can it be any better tomorrow?

                  Comment


                  • #10
                    Re: statistics question

                    "A jury of one's peers" is what comes to mind.
                    bigmrg74: "You can't drink the day away if you don't start early!"
                    SledDog: "UncleRay seems to be the most sensible one here tonight."
                    All great men are dead and I'm not feeling well.
                    A Margarita! in every hand and another Margarita! in the other hand!

                    And stay off the lawn!

                    Comment


                    • #11
                      Re: statistics question

                      Originally posted by gopheritall View Post
                      Those darn left handed people always stick together!
                      Good guess, but no.

                      Originally posted by LynahFan View Post
                      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.
                      Last edited by unofan; 02-29-2012, 10:45 PM.

                      Comment


                      • #12
                        Re: statistics question

                        Originally posted by gopheritall View Post
                        Those darn left handed people always stick together!
                        Dang straight we do! We're in our right minds.

                        Comment


                        • #13
                          Re: statistics question

                          Originally posted by gopheritall View Post
                          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.
                          Last edited by Kepler; 03-01-2012, 10:26 AM.
                          Cornell University
                          National Champion 1967, 1970
                          ECAC Champion 1967, 1968, 1969, 1970, 1973, 1980, 1986, 1996, 1997, 2003, 2005, 2010
                          Ivy League Champion 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1977, 1978, 1983, 1984, 1985, 1996, 1997, 2002, 2003, 2004, 2005, 2012, 2014, 2018, 2019, 2020

                          Comment


                          • #14
                            Originally posted by UncleRay View Post
                            "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
                            I believe in life, and I believe in love, but the world in which I live in keeps trying to prove me wrong.

                            Comment


                            • #15
                              Re: statistics question

                              Originally posted by LynahFan View Post
                              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.
                              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.
                              Last edited by Patman; 03-01-2012, 11:09 AM.
                              BS UML '04, PhD UConn '09

                              Jerseys I would like to have:
                              Skating Friar Jersey
                              AIC Yellowjacket Jersey w/ Yellowjacket logo on front
                              UAF Jersey w/ Polar Bear on Front
                              Army Black Knight logo jersey


                              NCAA Men's Division 1 Simulation Primer

                              Comment

                              Working...
                              X