The Artsy Corporation has been sued in the United States Federal Court on charges of employment discrimination under Title VII of the Civil Rights Act of 1964. (Artsy is an actual corporation and the data given in the case is real, but the name has been changed to protect the firm's true identity.) The litigation at contention here is a "class action" lawsuit brought on behalf of all females whom the company employed, or who had applied for work with the company, between 1979 and 1987. Artsy operates in several states, runs four quite distinct businesses, and has many different types of employees. The allegations against Artsy include issues of hiring, pay, promotions, and other "conditions of employment."

In such large class action employment discrimination lawsuits statistical evidence commonly plays a central role in the determination of guilt or damages. In an interesting twist on traditional legal procedures, the precedent in these cases is that plaintiffs may make a "prima-facie" case purely in terms of circumstantial statistical evidence. If that statistical evidence is reasonably strong, the burden of proof shifts to the defendants to rebut the plaintiff's statistics with other statistical data, other statistical analyses of the same data, or by non-statistical testimony. In practice, statistical arguments often dominate the proceedings of such EEO cases. Indeed, in this case the statistical data used filled numerous computer tapes and the supporting statistical analysis comprised thousands of pages of computer printouts and reports. We work here with a small subset of the voluminous data that pertain to one of the several contested issues in one of the company's locations.

The data in the accompanying file relate to the pay of 256 employees on the bi-weekly payroll at one of the Artsy Companys Pocahontas, Maine production facilities. The data include: an identification number, the person's gender, F or M, the person's job grade in 1986, the length of time (in years) the person had been in that job grade as of 31 December 1986, and the person's weekly pay rate as of 12/31/86.

These data permit a statistical examination of one of the issues in the case - fair pay for female employees.

The plaintiff's attorneys have proposed settling the pay issues for this group of female employees for a "back pay" lump payment of 25% of their pay during the period 1979 to 1987. It is your task to examine the data in the table for evidence in favor of, or against the charges of pay discrimination against the females. You have been hired to advise the lawyers for the Artsy Company on how to proceed.

Please consider the following issues:

1) Overall, how different is pay by gender? Are the differences in pay statistically significant? Does a statistical significance test have meaning in a case like this? If so, how should it be performed? Lay out as succinctly as possible the arguments that you anticipate the plaintiffs will make with this data set.

2) The Artsy Company wishes to argue that a legitimate explanation of the pay rate differences may be the difference in job grades by gender. (In this analysis we tacitly assume that each person's job grade is, in fact, appropriate for them, even though the plaintiff's attorneys have charged that females have been unfairly kept in the lower grades. Other statistical data, not available here, are used in the analysis of the job placement issue.) The companys lawyers ask, "Is there a relatively easy way to understand, to analyze and display the pay differences by job grade? Is it easy enough that it could be presented to an average jury without confusing them? Again, use the data to anticipate the possible arguments of the plaintiffs. To what extent does job grade appear to explain the pay rate differences between the genders? Propose and carry out appropriate hypothesis tests or confidence intervals to check whether the difference in pay between genders is statistically significant within each of the grades.

3) In the actual case, the analysis carried out in (2) above suggested to the attorneys that differences in pay rates are due, at least in part, to differences in job grades. They had heard that in another EEO case the dependence of pay rate on job grade had been investigated with regression analysis. Perform a regression of pay rate on job grade. Interpret the results fully. Is the regression significant? How much of the variability in pay does job grade account for? What light does this analysis shed on the pay fairness issue? Does it help or hurt the Artsy Company? Is it fair to the female employees?

4) It is argued that seniority within a job grade should be taken into account because the Artsy Company's written pay policy explicitly calls for the consideration of this factor. How different are times in grade by sex? Are they enough to matter?

5) The Artsy legal team wants an analysis of the simultaneous influence of grade and time in grade on pay. Perform a regression of pay rate versus grade and time in grade. Is the regression significant? How much of the variability in pay rates does this model explain? Will this analysis help your clients? Could the plaintiffs effectively attack it? Consider residuals in your analysis of these issues.

6) The attorneys ask: Is it possible to do a regression analysis that simultaneously considers the effect on pay of grade, time-ingrade and sex? If so, carry one out.

Organize your analyses and conclusions in a brief presentation summarizing your findings for your client, the Artsy Corporation. Be complete but succinct. Be sure to advise them on the issue of the settlement. Please be as forceful as you can be in arguing "the Artsy Case" without misusing the data or statistical theory. Apprise your client of the risks they face by developing the most forceful counter argument that you believe the female plaintiffs could fairly make.