Approaches for Dealing with Small Sample Sizes in Employment Discrimination Litigation

Piette, Michael J., White, Paul F., Journal of Forensic Economics

I. Introduction

The statistical analysis of allegations of employment discrimination has become increasingly more commonplace in the courtroom during the last two decades. Whether a result of claims of discrimination on the basis of race, gender, or national origin (Title VII of the Civil Rights Act), age (Age Discrimination in Employment Act) or disability (Americans with Disability Act), statistical support of the alleged discrimination is often an integral part of the litigation process. Statistics are also utilized in an increasing proportion of the smaller, single-plaintiff or multiple-plaintiff suits where the plaintiff(s) has claimed that a "pattern and practice" of discrimination has occurred. There is a rich literature focusing on the use of statistical analysis as applied to employment discrimination. That literature includes the broad-base reviews found in the major economics journals and texts, the merging of law and economics/statistics contained in the law reviews, and the articles of a more applied nature published in the forensic economics journals.

The use of statistical analysis outside of the class action or large, multiple plaintiff arena presents particular problems for economists and applied statisticians, many of which have not been addressed in the forensics economics literature in a systematic fashion. In particular, a main problem area concerns the reliability of statistical inference in allegations of discrimination in a selection process (hire, promotion, termination) as the sample size or group of individuals in the analysis becomes smaller and smaller. The purpose of this paper is to discuss several techniques for analyzing allegations of employment discrimination with small sample sizes.

The paper is organized as follows. Part II illustrates the methodological approach to a typical employment discrimination case. In Part III, the mathematics of analyzing employment discrimination is discussed and an example of an employment selection decision is provided. Part IV indicates several of the approaches that have been used in actual litigation for addressing the small sample size problem. Part V discusses the difference between "statistical significance" and "practical significance," an important consideration in this area. Summary and concluding comments are offered in Part VI of the paper.

II. The Methodology of Analyzing Allegations of Employment Discrimination

In an employment or labor market context, discrimination is typically associated with the "selection process" or the "selection decision." Within a given selection process, discrimination is present when the process confers benefits (or imposes burdens) on one group but not on the other, given that both groups are similarly situated with respect to all salient characteristics except race, age, gender, or other attributes protected under the law.(1) Selection decisions are made at the time an individual is recruited or subsequently hired, during the course of his or her employment, and at the point of termination.

For example, if there is bias in a promotion decision, equally productive men and women with similar preferences for promotional opportunities will not be promoted at similar rates relative to their representation in the prepromotional pool. In other words, the representation of men and women after a promotion selection will not be approximately equal to their representation in the pool of promotion candidates. Every selection process has two sides regardless of the type of selection process under consideration--those available for selection (the input side) and those selected (the output side).

The first step in the analysis of employment discrimination is to model the employment process in question. This often involves the identification of the appropriate employee pools, which leads to the construction of a benchmark. A benchmark is a reference point to which selection events are compared. For example, in gender or race discrimination cases, the benchmark is commonly the distribution of women or minorities in the labor pool (company, plant, job group) to which the distribution of the selectees (those hired, promoted, or terminated) are compared.

In the analysis of employment discrimination claims, statistical tests are used to develop a meaningful comparison of "what actually happened" and "what would have been expected to happen" if a particular selection process was either random or neutral with respect to the characteristics of the protected class. However, even if discrimination was not present, the comparison of what did happen with what would have happened in the absence of discrimination will never be perfect. There will nearly always be some disparity between the actual and the predicted number of selections. This disparity, commonly called chance variability, requires the Court to determine a level of significance they are willing to accept when distinguishing between statistical proof of discrimination compared to random chance.(2) Therefore, setting the level of significance is the second step in analyzing allegations of employment discrimination.

Although the choice of a particular level of significance is subjective, legal precedent is clearly the overriding consideration. One standard is the 5% significance level, which may also be referred toby its counterpart, the 95% confidence level.(3) The Supreme Court, in a landmark case involving the selection of minorities to serve on grand juries (Castaneda v. Partida, 1977) stated "... if the difference between the expected value and the observed number is greater than two or three standard deviations," then the process we are observing is unlikely to have occurred by chance alone. This "rule" was quickly applied to the employment discrimination area in Hazelwood School District v. U.S. (1977) and became known as the "Hazelwood Standard." Under this standard, Courts have accepted as statistical "proof" of discrimination evidence (other things equal) suggesting that there is less than a 5% probability (about two standard deviations for a two-tailed test), or less …

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Publication information: Article title: Approaches for Dealing with Small Sample Sizes in Employment Discrimination Litigation. Contributors: Piette, Michael J. - Author, White, Paul F. - Author. Journal title: Journal of Forensic Economics. Volume: 12. Issue: 1 Publication date: Winter 1999. Page number: 43. © 1999 National Association of Forensic Economists. COPYRIGHT 1999 Gale Group.

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