TalkLeft Discussion Forums
George Zimmerman Trial Coverage => Jury Selection => Jurors Passed for Cause, Round 1 => Topic started by: TalkLeft on June 19, 2013, 12:07:42 PM

from one media outlet: June 1011
(http://i311.photobucket.com/albums/kk453/TalkLeft/zimmerman/gzjury%20round1/june10and11_zpsa0b3e378.jpg)

June 1214
(http://i311.photobucket.com/albums/kk453/TalkLeft/zimmerman/gzjury%20round1/june12to14_zps50d6dbaa.jpg)

June 17 and 18
(http://i311.photobucket.com/albums/kk453/TalkLeft/zimmerman/gzjury%20round1/june17and18_zpscc107c26.jpg)

The following analysis is based on twotailed, exact binomial tests of the sample of 40 jurors.
Race or Gender Proportion of population Proportion of Jury 90% Confidence Interval pvalue

White 0.658 0.650 (26 of 40) 0.5080.774 1
Black 0.117 0.175 (7 of 40) 0.0850.304 0.224
Hispanic 0.177 0.100 (4 of 40) 0.0350.214 0.298
Female 0.516 0.600 (24 of 40) 0.4580.731 0.343
Male 0.484 0.400 (16 of 40) 0.2690.542 0.343
At the 90% confidence level there is no statistically significant difference between any of the proportions of the jurors and the proportions of the population in Seminole County.

I have no idea what you mean, since I don't know math other than how to add, subtract, multiply, divide and do percentages. I'm sure I'm not alone. Isn't it simpler to just say:
According to the 2012 U.S. census (http://quickfacts.census.gov/qfd/states/12/12117.html), using 2011 figures, 81.6% of Seminole County is White and 11.7% is Black. They list:
White persons reporting only one race, 81.6%
White persons not Hispanic 65.8%
Black persons, 11.7%
Persons of Hispanic or Latino Origin 17.7%
(Hispanics may be of any race, so also are included in applicable race categories.)
Persons reporting two or more races 2.2%
American Indian and Alaska Native persons 0.4%
Asian persons, 3.9%
Native Hawaiian and Other Pacific Islander persons, 0.1%
There were 40 people chosen
26 are white (nonmixed race), or 61%, as compared to the county's white population (86% total, 66% nonHispanic)
7 or 8 are black  either 17% or 20%, as compared to the county's black population (12%)
It does seem that whites are underrepresented and blacks are overrepresented when compared to the census figures. If you are saying that there is statistically no difference between 12% and 17 or 20%, I don't see how that can be accurate.
Feel free to translate your method into language we can all understand. You may be right, it's just hard to credit something we've never heard of and have no idea what it is.

Feel free to translate your method into language we can all understand. You may be right, it's just hard to credit something we've never heard of and have no idea what it is.
Anytime there is a random draw from a pool of "chance" (the actual probability distribution in the community as a whole), the draw or sample (the venire) can deviate from the pool (the county). What is the chance of drawing EXACTLY the same percentages of each group to make the venire? Not very high. But, the venire/draw will probably be CLOSE to the makeup of the county/pool. But, the venire/draw COULD be quite different from the county/pool, just not likely.
How close a match is "probable" and how far from matching is "not likely" are (quantifiable) probability questions. The terms "confidence interval" and "pvalue" are terms used in probability and statistical analysis. At this point, if you don't understand the table and terms, it's safe to ignore them. I understand the table, and it's an interesting statistical analysis  but understanding isn't necessary.
If there is a need for some sort of proof that the racial makeup of the venire is a (close enough) match with the racial makeup of the county, then the onus is on the law to define what "close enough" is, and to justify that limitation.

Thanks. Let me try to explain the numbers, but first I want to discuss the issue of "white" versus "white notHispanic". Most every PJ list I have seen categorizes the PJs as Hispanic or White and not both. If those are mutually exclusive categories we must compare the PJs to the white and not Hispanic percentage in the census data. So by my count there are 26 "white and not Hispanic" PJs. There are 30 "white including Hispanic" jurors.
With my numbers, wherever I have written proportion, you can multiply by 100 to get percentage. So our Seminole County population numbers agree: 65.8%,11.7%, and 17.7% for White(not H), Black, and Hispanic.
Let me start with the black percentage as an example. Suppose you put every person's name in Seminole County on individual slips of paper and put them in a very large hat. If you picked 40 people at random out of the hat, you could by chance draw 40 black people or you could draw 0 black people, but both of these possibilities are highly unlikely. The most probable draw would be 5 black people (0.117 x 40 =4.68). Fortunately, we know using simple probability theory the exact probability of drawing each number of black people in a draw of 40. The analysis that I have run says that 90% of the time we would draw between 8.5% (about 3 black people) and 30.4% (about 12 black people). The bottom line is that it would not be unusual to draw between 3 and 12 black people when 40 people are chosen from the large hat of Seminole County residents. It would be unusual to draw 0,1,2, or greater than 12 black people.
I hope this helps because the 90% confidence interval column that I gave directly answers your question as to whether 7 or 8 black jurors is unusually high. It is not.
If my analysis still does not make much sense, I am more than willing to try again.
Incidently, this same analysis is used to report margins of error in polling data.

Incidently, this same analysis is used to report margins of error in polling data.
I think the analogy with public opinion polls is a good way to get a feel for this issue.
If it were to be expected that a sample of 40 would closely reflect the population it is drawn from, polling firms would poll samples of 40 people, instead of spending the money to poll samples of hundreds or a thousand. It's my understanding that a sample size of about a thousand is considered optimal, while a bare minimum would be something like 400 to 500. If a polling firm could get reliable results with smaller samples, they surely would.

I messed up slighltly in my explanation of the confidence interval in the post above. I cannot modify that post any more. So read this one instead.
Thanks. Let me try to explain the numbers, but first I want to discuss the issue of "white" versus "white notHispanic". Most every PJ list I have seen categorizes the PJs as Hispanic or White and not both. If those are mutually exclusive categories we must compare the PJs to the white and not Hispanic percentage in the census data. So by my count there are 26 "white and not Hispanic" PJs. There are 30 "white including Hispanic" jurors.
With my numbers, wherever I have written proportion, you can multiply by 100 to get percentage. So our Seminole County population numbers agree: 65.8%,11.7%, and 17.7% for White(not H), Black, and Hispanic.
Let me start with the black percentage as an example. Suppose you put every person's name in Seminole County on individual slips of paper and put them in a very large hat. If you picked 40 people at random out of the hat, you could by chance draw 40 black people or you could draw 0 black people, but both of these possibilities are highly unlikely. The most probable draw would be 5 black people (0.117 x 40 =4.68). Fortunately, we know using simple probability theory the exact probability of drawing each number of black people in a draw of 40. The analysis that I have run says that 90% of the time when we do get a draw 7 black people, the percentage of people in the full Seminole population will be between 8.5% and 30.4%. The true Seminole population percentage 11.7% falls within these confidence limits (8.5% and 30.4%). Thus, the result of drawing 7 black people at random from the large hat would not be unusual.
The bottom line is that if the "Proportion of population" falls within the "90% Confidence Interval", it is not an unexpected result.
I hope this helps because the 90% confidence interval column that I gave directly answers your question as to whether 7 black jurors is unusually high. It is not.
If my analysis still does not make much sense, I am more than willing to try again.
Incidently, this same analysis is used to report margins of error in polling data.

I think the analogy with public opinion polls is a good way to get a feel for this issue.
If it were to be expected that a sample of 40 would closely reflect the population it is drawn from, polling firms would poll samples of 40 people, instead of spending the money to poll samples of hundreds or a thousand. It's my understanding that a sample size of about a thousand is considered optimal, while a bare minimum would be something like 400 to 500. If a polling firm could get reliable results with smaller samples, they surely would.
Great point.
If you polled 40 people at random from Seminole County and asked "Are you black?" The margin of error that a polling firm would report is plus or minus 15%.
So if 7 out of 40 said yes, the poll percentage would be reported as 17.5% black with a margin of error of 15%.

So if 7 out of 40 said yes, the poll percentage would be reported as 17.5% black with a margin of error of 15%.
And it would not be statistically "unusual" (a clinically quantifiable conclusion) to have 10 of 40 say yes  resulting in a report of 25% black with the same margin of error.
BTW, your table has a pvalue of 1 in the first row. I suspect you've noticed that ;)

Thanks for the explanations. I'll defer to your expertise on the issue.

Just for the purpose of explanation, it's also important to note that the current venire isn't a random sample, since it excludes those dismissed for contact with pretrial publicity/formed and opinion/said the magic words/postponed jury duty, etc.. These factors introduce bias into the sample. The math shows it acts fairly similar to a random sample, though.

And it would not be statistically "unusual" (a clinically quantifiable conclusion) to have 10 of 40 say yes  resulting in a report of 25% black with the same margin of error.
BTW, your table has a pvalue of 1 in the first row. I suspect you've noticed that ;)
p=1 is correct in the exact binomial test when you hit the most probable number of people based on your hypothesized population.
I just ran the numbers and 9 black and above people would be statistically unusual.
The margin of error used by polling firms assumes the normal approximation to the binomial distribution. When you have small sample sizes, as we have in or jury example, you must revert back to the binomial distribution. The binomial becomes quite nonsymmetrical when the proportions approach zero or one.

What no one here seems to have taken into account is the age and citizenship demographics of Seminole County. The census numbers are for all persons, and includes those too young to serve on a jury and those who are too old. Also, the census counts noncitizens and felons, who, as far as I know are not eligible to serve on a jury.
I presume, but have no data, that each demographic group has a different percentage of young (or very old) people. That would certainly skew the data. Just my 2 cents. Although I don't generally post here, I certainly do appreciate the high level of discussion on TalkLeft and have been following this case closely.

Welcome to the board, AP. I agree  your previous post raises some great points. I think it still worthwhile to compare this venire to the overall population (even considering selection bias) just to get a feel for the fairness or at least the perception of fairness of that process.
The final jury is a tougher nut  the small sample size and the advocate's selection of which jurors to strike make it much less useful  though I guess one could still glean information from the comparison as a complete hypothetical.

What no one here seems to have taken into account is the age and citizenship demographics of Seminole County. The census numbers are for all persons, and includes those too young to serve on a jury and those who are too old. Also, the census counts noncitizens and felons, who, as far as I know are not eligible to serve on a jury.
I presume, but have no data, that each demographic group has a different percentage of young (or very old) people. That would certainly skew the data. Just my 2 cents. Although I don't generally post here, I certainly do appreciate the high level of discussion on TalkLeft and have been following this case closely.
An excellent first post.
I agree with your comments. One could go back to the raw census data and modify the numbers we have been using in the manner you suggest.