Artsy Corporation has been sued in U.S. Federal Court on charges of sex discrimination in employment under Title VII of the Civil Rights Act of 1964.7 The litigation at contention here is a class-action lawsuit brought on behalf of all females who were employed by the company, 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 of the plaintiffs deal with issues of hiring, pay, promotions, and other "conditions of employment."

In such large class-action employment discrimination lawsuits, it has become common for statistical evidence to play a central role in the determination of guilt or damages. In an interesting twist on typical legal procedures, a precedent has developed in these cases 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 plaintiffs' statistics with other data, other analyses of the same data, or nonstatistical testimony. In practice, statistical arguments often dominate the proceedings of such Equal Employment Opportunity (EEO) cases. Indeed, in this case the statistical data used as evidence filled numerous computer tapes, and the supporting statistical analysis comprised thousands of pages of printouts and reports. We work here with a typical subset that pertains to one contested issue at one of the company's locations.

The data in the file C11_01.xlsx relate to the pay of 256 employees on the hourly payroll at one of the company's production facilities. The data include an identification number (ID) that would identify the person by name or social security number; the person's gender (Gender), where 0 denotes female and 1 denotes male; the person's job grade in 1986 (Grade); the length of time (in years) the person had been in that job grade as of December 31, 1986 (Time in Grade); and the person's weekly pay rate as of December 31, 1986 (Rate). These data permit a statistical examination of one of the issues in the case-fair pay for female employees. We deal with one of three pay classes of employees-those on the biweekly payroll at one of the company's locations at Pocahantas, Maine.

The plaintiffs' attorneys have proposed settling the pay issues in the case for this group of female employees for a "back pay" lump payment to female employees of 25% of their pay during the period 1979 to 1987. It is your task to examine the data statistically for evidence in favor of, or against, the charges. You are to advise the lawyers for the company on how to proceed. Consider the following issues as they have been laid out to you by the attorneys representing the firm:

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 company wishes to argue that a legitimate explanation of the pay-rate differences may be the difference in job grades. (In this analysis, we will tacitly assume that each person's job grade is, in fact, appropriate for him or her, even though the plaintiffs' attorneys have charged that females have been unfairly kept in the lower grades. Other statistical data, not available here, are used in that analysis.) The lawyers ask, "Is there a relatively easy way to understand, 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 previous analysis 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 simple linear regression of pay rate on job grade for them. Interpret the results fully. Is the regression significant? How much of the variability in pay does job grade account for? Carry out a full check of the quality of your regression. What light does this shed on the pay fairness issue? Does it help or hurt the 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 company's written pay policy explicitly calls for the consideration of this factor. How different are times in grade by gender? Are they enough to matter?

5. Artsy's legal team wants an analysis of the simultaneous influence of grade and time in grade on pay. Perform a multiple regression of pay rate versus grade and time in grade. Is the regression significant? How much of the variability in pay rates is explained by this model? Will this analysis help your clients? Could the plaintiffs effectively attack it? Consider residuals in your analysis of these issues. 6. Organize your analyses and conclusions in a brief report summarizing your findings for your client, Artsy Corporation. Be complete but succinct. Be sure to advise them on the settlement issue. 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 showing them the forceful and legitimate counterargument the female plaintiffs could make.