Statistical Analysis As Evidence in Employment Discrimination

Slide 1: 

Statistical Analysis as Evidence in Employment Discrimination Litigation presented by Stephanie R. Thomas, Ph.D. sthomas@thomasecon.com Thomas Econometrics Silver Lake Executive Campus 41 University Drive, Suite 400 Newtown PA 18940 215-642-0072 www.thomasecon.com

Agenda : 

Agenda Alternative Legal Theories of Discrimination Disparate Treatment Disparate Impact Direct versus Indirect Evidence Basics of Statistical Inference Statistical Significance and Sample Size Application of Statistical Inference to Disparate Impact and Disparate Treatment Claims Single Pool Analysis – example and underlying assumptions Multiple Pools Analysis – example and underlying assumptions The Importance of Statistics: Randall v. Rolls Royce

Alternative Legal Theories : 

Alternative Legal Theories Disparate Treatment: intentional discrimination because of race, gender, age, etc. (‘traditional discrimination’) Disparate Impact: facially-neutral policy or practice disproportionately screens out protected class members (e.g., college degree requirement for employment) The form of the statistical analysis presented depends upon the legal theory involved

Disparate Treatment : 

Disparate Treatment Demonstration of intent is critical Statistical evidence is more relevant in a class setting (versus an individual plaintiff setting) Plaintiffs’ objective is to show that, among similarly situated individuals, outcomes are adversely statistically significantly correlated with membership in a protected group Analysis is often complex in order to capture the essence of “similarly situated”

Disparate Impact : 

Disparate Impact Intent is irrelevant Purely a statistical question – did the challenged policy or practice have a disproportionate adverse impact on the protected group? If yes, then demonstrate the validity of the practice If no, then end of the story Typically, a very straightforward statistical analysis

The Basics of Statistical Inference : 

The Basics of Statistical Inference The wager: flip a coin 10 times I pay you $1 for every tail you pay me $1 for every head I go behind a screen and flip the coin 10 times I come back out, report getting 10 heads, and demand $10 Your Challenge: Have you been cheated? What evidence do you have? Direct evidence or indirect evidence

Direct Evidence of Cheating : 

Direct Evidence of Cheating Security camera videotaping me behind the screen – reveals that I lied (I actually got 6 heads) Coin is two-headed Coin is weighted towards heads What if no direct evidence exists?

Indirect Evidence of Cheating : 

Indirect Evidence of Cheating The probability of a head on any flip of a fair coin is 50% We would expect 5 heads in 10 flips: (10 * 50% = 5) The reported result of 10 heads is five more than expected – a surplus of 5 heads Is this disparity large enough to doubt that simple chance was the cause?

Probability Distribution : 

Probability Distribution In 10 flips, we would expect 5 heads More often than not, we won’t get exactly 5 heads in 10 flips How likely is it that we would get: 6 heads? 7 heads? 8 heads ? 9 heads? 10 heads? To answer this question, we can use probability

Probability Distribution : 

Probability Distribution

The Normal Distribution : 

The Normal Distribution

Probability Distribution : 

Probability Distribution Deviations from “expected” results can occur due to chance factors It’s possible that you were not cheated 10 heads is expected to occur once in 1,000 games Is the observed outcome a sufficiently ‘rare’ result to conclude that chance is not the likely explanation?

Probability Distribution : 

Probability Distribution Where do we draw the line? Hazelwood School District v US (1977): a disparity of at least “2 or 3” standard deviations is “statistically significant”… shifts the burden to the employer

What Inference Do We Draw? : 

What Inference Do We Draw? The probability of 10 heads in 10 flips of a fair coin is 0.001, or 1 in 1,000, or 3.10 units of standard deviation This satisfies the Hazelwood threshold of “2 or 3 units” of standard deviation The difference between “actual” and “expected” is statistically significant You would reject the null hypothesis of a fair game and accuse me of cheating

Statistical Significance : 

Statistical Significance No valid adverse inference can or should be drawn if the disparity is not statistically significant A disparity that is not statistically significant is statistically equivalent to zero

Statistical Significance and Sample Size : 

Statistical Significance and Sample Size Statistical significance is a function of: The size of the disparity The number of things being studied For example, consider the following:

Statistical Significance and Sample Size : 

Statistical Significance and Sample Size

Application of Statistical Inference : 

Application of Statistical Inference The application of statistical inference will differ depending on whether we are studying questions of disparate impact or disparate treatment

Application of Statistical Inference:Disparate Impact Claims : 

Application of Statistical Inference:Disparate Impact Claims Example Analysis of Hiring 1,000 applicants 500 white (50%) 500 nonwhite (50%) 200 hire events 120 white 80 nonwhite

Example Analysis of Hiring : 

Example Analysis of Hiring 50% of applicants are NW Expected NW hires = 100 (200 x 50%) NW shortfall = 20 (100 expected – 80 actual) Statistically significant at 3.09 s.d. Follow-up is needed

Example Analysis of Hiring : 

Example Analysis of Hiring Assume the follow-up reveals the following: One of the requirements for the position in question is a particular degree Whites are more likely to have this particular degree than non-whites Non-whites are disproportionately “screened out” because of this degree requirement The analysis is repeated using “qualified applicants”

Example Analysis of Hiring : 

Example Analysis of Hiring 30% of qualified applicants are NW Expected NW hires = 60 (200 x 30%) NW shortfall = -20 (60 expected – 80 actual) Favors NWs – there is a surplus of NW hires

Example Analysis of Hiring : 

Example Analysis of Hiring Analyses reveal the following: Statistically significant shortfall of NW hires among all applicants Surplus of NW hires among “qualified” applicants The business necessity and “job related-ness” of this degree requirement for this particular position needs to be established

Application of Statistical Inference:Disparate Treatment Claims : 

Application of Statistical Inference:Disparate Treatment Claims Example Analysis of Promotions 1,000 candidates 500 male (50%) 500 female (50%) 200 promotion events 120 male 80 female

Example Analysis of Promotions : 

Example Analysis of Promotions 50% of employees are female Expected female promotions = 100 (200 x 50%) Female shortfall = 20 (100 expected – 80 actual) Statistically significant at 3.09 s.d.

Assumptions in Previous Promotions Example : 

Assumptions in Previous Promotions Example All employees compete against one another for promotion “Qualification” factors are identically distributed by gender (this is the broadest possible view of “similarly situated”) Assumes one single pool with everyone having an equal likelihood of bring promoted

Example Analysis of Promotions : 

Example Analysis of Promotions

“Multiple Pools” Analysis : 

“Multiple Pools” Analysis All employees are not competing with each other; each employee is only competing with others in her “pool” Within each pool, we see gender parity Pools can be jobs, pay grades, locations, etc. However, pools must be justified!

Another Multiple Pools Example : 

Another Multiple Pools Example

Application of Statistical Inference : 

Application of Statistical Inference Remember that statistical analysis can never PROVE discrimination We can only say that the inferences drawn from our statistical analyses either are or are not consistent with the hypothesis of discrimination

The Importance of Statistics : 

The Importance of Statistics Randall et al. v. Rolls Royce Corporation, No. 06-cv-860-SEB-JMS

The Importance of Statistics:Randall v. Rolls Royce : 

The Importance of Statistics:Randall v. Rolls Royce Sally Randall and Rona Pepmeier – high level female managers Claimed: Paid less than male counterparts Passed over for promotions Witnessed male executives putting down women Plaintiffs seeking class certification

The Importance of Statistics:Randall v. Rolls Royce : 

The Importance of Statistics:Randall v. Rolls Royce In March 2010, Hon. Sarah Evans Barker of the US District Court for the Southern District of Indiana denied certification of a putative gender discrimination class claim.

The Importance of Statistics:Randall v. Rolls Royce : 

The Importance of Statistics:Randall v. Rolls Royce Judge Barker’s decision: thorough analysis of competing statistical evidence before the court Decision highlights the significance of powerful expert reports and testimony in class action litigation

The Importance of Statistics:Randall v. Rolls Royce : 

The Importance of Statistics:Randall v. Rolls Royce “If there is a dispute as to the value or applicability or efficacy of either side’s expert statistical analysis, the way in which that dispute is resolved impacts both the underlying systemic discrimination claim and the determination of whether a viable class action exists.”

The Importance of Statistics : 

The Importance of Statistics Attorneys with an understanding of statistical analyses and the inferences drawn from these analyses: Are better positioned to advise their clients on the merits of the matter Are more effective during pretrial preparation phase of the case

The Importance of Statistics : 

The Importance of Statistics Basic quantitative skills allow the attorney to: Understand the analyses that will be appropriate for the matter at hand Speculate about what statistical analyses might be presented by opposing counsel Anticipate potential attacks on the statistical analyses she presents All of these lead to a more effective presentation at trial

The Importance of Statistics : 

The Importance of Statistics A basic familiarity with common statistical concepts and techniques as applied to law will allow attorneys to better serve their clients and to participate in meaningful discussions with their experts

Conclusion : 

Conclusion Alternative Legal Theories of Discrimination Disparate Treatment versus Disparate Impact Basics of Statistical Inference Statistical Significance Application of Statistical Inference to Disparate Impact and Disparate Treatment Claims The Importance of Statistics

Slide 40: 

Statistical Analysis as Evidence in Employment Discrimination Litigation presented by Stephanie R. Thomas, Ph.D. sthomas@thomasecon.com Thomas Econometrics Silver Lake Executive Campus 41 University Drive, Suite 400 Newtown PA 18940 215-642-0072 www.thomasecon.com