Statistical Sophistication Would Have Provided A Different Liability Answer

|||Statistical Sophistication Would Have Provided A Different Liability Answer

Statistical Sophistication Would Have Provided A Different Liability Answer

October 2013

Economists and other financial experts are often hired to assess damages, assuming that liability will be proven.  However, liability it self can sometimes be established or disproven based on statistics.

For example, in a recently affirmed case involving employment discrimination, the application of a simple method failed to provide the Court with information that would likely have changed their decision.  The Federal Court (and the Sixth Circuit Court of Appeals) concluded employer discrimination against protected classes occurred based on a simple calculation commonly referred to as the “four-fifths rule” or the “80% rule”.  In contrast, more rigorous statistical methods suggest otherwise and the City of Akron, Ohio may have been unfairly penalized.

Employers who employ standardized tests to hire and/or promote candidates must ensure that such tests do not adversely impact protected classes.  In Howe v. City of Akron, Case No. 11-3752 (6th Cir. July 22, 2013) the issue was whether the City of Akron’s fire department used procedures to promote candidates to lieutenant and captain that were prejudicial.  Plaintiffs were allowed to exclusively rely upon the “four-fifths” rule to establish adverse impact.  The U.S. EEOC’s describes this simplistic four-fifths guideline of testing for adverse impact, but also warns against weaknesses in its application:

“A selection rate for any race, sex, or ethnic group which is less than four-fifths (4/5) (or eighty percent) of the rate for the group with the highest rate will generally be regarded by the Federal enforcement agencies as evidence of adverse impact, while a greater than four-fifths rate will generally not be regarded by Federal enforcement agencies as evidence of adverse impact. … Greater differences in selection rate may not constitute adverse impact where the differences are based on small numbers and are not statistically significant

[emphasis added]

Using this rule, Plaintiffs convinced the Court that African-Americans and those over 40 were being unfairly treated in the Akron fire department with respect to Lieutenant promotions.  The data and calculations follow:

Table 1:  Four-fifths (aka 80%) test suggests African American don’t get enough Lieutenant promotions

Promoted

Not Promoted

Total

Adverse Impact Ratio

Pass 80% test?

Caucasian

25

44

69

25 / 69 = 36%

NO, because 55% is less than 80%

African American

3

12

15

3 / 15 = 20%

Total

16

56

84

20% / 36% = 55%

 

Table 2:  Four-fifths (aka 80%) test suggests those over 40 don’t get enough Lieutenant promotions

Promoted

Not Promoted

Total

Adverse Impact Ratio

Pass 80% test?

Over 40

7

22

29

7 / 29 = 24%

NO, because 63% is less than 80%

Under 40

21

34

55

21 / 55 = 38%

Total

28

56

84

24% / 38% = 63%

 

Based on the above results, the Plaintiff prevailed.  Interestingly, although not a case involving discrimination against Caucasians, the same simple test shows that Caucasians were suffering discrimination specific to Captain level promotions, as follows:

Table 3: Four-fifths (aka 80%) test suggests Caucasians don’t get enough Captain promotions

Promoted

Not Promoted

Total

Adverse Impact Ratio

Pass 80% test?

Caucasian

7

19

26

7 / 26 = 27%

NO, because 38% is less than 80%

African American

5

2

7

5 / 7 = 71%

Total

12

21

33

27% / 71% = 38%

 

However, if the more statistically robust and commonly-accepted chi-square and Fisher Exact statistical tests (accepted by the U.S. Equal Employment Opportunity Commission (“EEOC”) and U.S. Department of Labor (“DOL”)) were used, the opposite conclusions would have been reached.  Both tests examine whether two groups (in this case, (i) race and age, and (ii) employees promoted or not promoted) are related, as follows:

  • The chi-square compares the “actual” values (values that actually were observed) with the “statistically expected” values (calculated values based on the sum of actual values that one would expect assuming the hypothesis is valid). Based on the differences between the actual values and the statistically expected values, the test result either accepts or rejects the hypothesis with a certain confidence level;
  • The Fisher exact test calculates the probability of getting deviations as extreme and more extreme as the “actual” values (values that actually were observed) under the null hypothesis that the two groups (e.g., race and employees promoted) are not related. Based on the probability result, the test result either accepts or rejects the hypothesis with a certain confidence level.

The results of these tests vary depending on the degree of certainty (aka confidence levels) ascribed.  See this article for more information about the chi-square and Fisher Exact tests.

In contrast to the Court’s decision, Table 4 below demonstrates that there is no statistically significant relationship between race and the promotion rates at the Lieutenant level (where the protected classes are allegedly being unfairly treated according to the four-fifths results in Tables 1 and 2 above).

Table 4:  Statistical analysis contradicts the Court’s ruling.

Alleged Discrimination

Four-fifths (80%) Test

Statistical Significance Tests

Chi-Square

Fisher Exact

Race

Fail

Pass

Pass

Age

Fail

Pass

Pass

These results are based on an 85%, 90%, and 95% confidence levels.  The appropriate confidence level and precision rate may vary based on the individual circumstances being assessed and the legal standard being applied.  While rigorous scientific analyses often use a 95% confidence level, lower confidence levels can appropriately be used to reach valid statistical conclusions in various practical applications.  For example, if the legal standard is a preponderance of the evidence, this standard is often presumed to be met if the proposition is more likely to be true than not true.

Because there is less than five data points in certain categories (see Table 3), the Fisher Exact may be a more accurate test than chi-square in this instance.  See the following article Chi-Square Tests Independence for more information about when the Fischer Exact test may be more accurate test than the chi-square test.

These tests are not limited to allegations of discrimination.  The chi-square and Fisher Exact tests can be used in nearly any situation in which one wants to evaluate whether variation between two groups is statistically significant.   

Fulcrum Inquiry performs statistical analyses and related expert testimony in employment and other disputes.  Additionally, Fulcrum provides a unique interactive lost earnings model that is suitable for settlement purposes.

 

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