Chi Square Calculator

The American legal system of criminal courts is predicated on the notion that an individual has the right to a trial by a jury of his peers. The Sixth Amendment to the United States Constitution states that, "In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the state and district wherein the crime shall have been committed." This means, inter alia, that characteristics of jury members should reflect characteristics of the general population of the judicial district.

However, in a number of cases in American legal history, there have been assertions of "jury fixing" in which the jury selection process has been tilted to obtain a jury that is overly favorable to the individual charged with the crime or overly unfavorable. Typically, such fixing occurs by selecting a jury whose characteristics are quite different from those of the population from which it is selected.

Many critics feel that the current jury selection process is unfair, producing jurors that do not represent the diversity of society. Further, they argue that jury member selection has become less random and more of an attempt by lawyers to build the "perfect jury" for their case.

Described below are two cases that ask you to draw upon the tools of the chi-square lesson in answering a set of questions.

Example 1

In a study in Alameda County, California, researchers compared the demographic characteristics of members of grand juries to determine how closely these juries reflected the population of the county. If the juries were selected randomly or impartially, then the characteristics of the jurors should closely match those of the larger county; however, if attorneys were tilting the jury selection process, then the jurors' characteristics would be quite different from the county. (figures taken from UCLA Law Review, vol 20, 1973 - as shown at: http://www.stat.ucla.edu/cases/jury/)

Age	Country-Wide %	# of Jurors
21-40	42	5
41-50	23	9
51-60	16	19
Older than 61	19	33
Total	100	62

Questions

Based on the figures shown in the table above, use the chi-square test to evaluate whether there is evidence of jury fixing in terms of the age of jurors in Alameda County.

What is the null hypothesis? What is the alternative hypothesis?

What figures do you need to calculate for this test?

How many degrees of freedom are there?

What is the value of the chi-square statistic for this table? What is the p-value of this statistic?

From this value, what can you conclude about the age of jurors in Alameda County?

Example 2

The same study of jurors in Alameda County, California, also found the following distribution of the education level of jurors:

Education Level	Country-Wide %	# of Jurors
Elementary Only	28.4	1
Secondary	48.5	10
Some College	11.9	16
College Degree	11.2	35
Total	100	62

Based on the figures shown in the table above, use the chi-square test to evaluate whether there is evidence of jury fixing in terms of the education level of jurors in Alameda County.

Questions

What is the null hypothesis? What is the alternative hypothesis?

What figures do you need to calculate for this test?

How many degrees of freedom are there?

What is the value of the chi-square statistic for this table? What is the p-value of this statistic?

From this value, what can you conclude about the education level of juries in Alameda County?

Example 3

An examination of data from the 1994 O.J. Simpson murder trial in Los Angeles, California tests the hypothesis that jury composition is not reflective of the population, or even the initial jury pool.

The 1990 Census shows that Los Angeles has the following characteristics in terms of residents' race:

Los Angeles County, CA
White	5,035,103
Black	992,974
American Indian, Eskimo, or Aleut	45,508
Asian or Pacific Islander	954,485
Other Race	1,835,094

Race	Percentage in City of Los Angeles
Black	14.0%
White	53.6%
Hispanic	22.8%
Asian	19.6%

Race	Percentage in Initial Jury Pool	Number of Jurors
Black	28	9
White	40	2
Hispanic	17	1
Asian	15	0

Questions

What is the null hypothesis? What is the alternative hypothesis?

What figures do you need to calculate for this test?

How many degrees of freedom are there?

What is the value of the chi-square statistic for this table? What is the p-value of this statistic?

Does the jury pool reflect a biased selection process?

Does the final jury chosen for the O.J. trial reflect a biased selection process?