Wouldn’t it be wonderful if there was a way to measure how unfair agency policies or practices are, especially if the measure was widely recognized as having evidentiary value? Of course it would because union leaders would be able to go to the bargaining table to argue with authority for changes to unfair HR systems such as those involving performance awards, promotions, appraisals, training and sick leave restrictions. Well, there is such a measurement and FEDSMILL describes how to use it below.

Let’s start with a problem. Suppose that you asked for a breakdown of how management has distributed the annual performance awards over the last two years and here is what you found.  364 of the 551 men in the office got them and 291 of the 537 women got them.  In simple percentages, 66% of the men and 54% of the women received awards. That is not even, but does it violate your contract or regulatory obligation to distribute them fairly and equitably?  Does it violate law? Here is one way to figure that out.

The Internet offers free calculators that merely require you to enter the four numbers in the second sentence above and then click the “Compute” button. Before you can blink four times, it will return a report that tells you whether or not there is court-approved statistical evidence suggesting that the women have been treated disparately in the eyes of the law.

Let’s try it. Go to’s favorite web calculator entitled, “Disparate Impact Analysis” and published by the folks at  Don’t be scared off by the statistical terminology; this is easier than third-grade long division.

Step 1 – Start in the upper right corner where the calculator asks you to “Select the type of employment decision.” The drop down menu offers three options; you really only need to use two. Select the “Promotion” option whenever you are trying to assess anything that employees view as positive, such as promotions, awards, choice assignments, etc. (Select the “Termination” option whenever measuring management decisions that are adverse to employees.)  For purposes of this example select the “Promotion” option.

Step 2 – Now move back to the left side where you see the words “Number of Males.” There are two boxes immediately below that you need to fill in. Enter the total number of men (551) in the box “Applicants,” because conceptually every male wanted an award, making them Applicants for purposes of this calculator.  In the box labeled “Selected” enter the number of men who were selected (364) for the award.

Step 3 – When finished move down to the two boxes below the words “Number of Females,” and enter their numbers.

Step 4 – Below the four boxes you just filled in is a list of five statistical tests. If each is not already checked, click it.

Step 5 – Now move to the right where you see a button labeled “Compute.” Click it and wait three or so seconds. The calculator will send you back a report that is invaluable for the union rep. It calculates the five statistical measures that arbitrators, EEOC, and the courts use substantially to decide whether any protected class (women, men, racial minorities or majorities, those 40 and over, etc.) suffered an unfair and/or illegal impact from how management distributed the award.

Now let’s focus on how to read the report produced.

Step 6 – The first statistic returned is the Adverse-Impact Report. The statistic is explained and then the statistical conclusion is reported in the white-background box. In our case it should say, “Adverse impact as defined by the 4/5ths rule was not found in the above data.”  If you want to know a little bit more about the 4/5ths Adverse Impact Ratio, check out the material from the folks at Workforce Dynamics. LLC or a zillion other pages that pop up when you search the term.

Step 7 – Next up is a Chi-Square Report. After displaying the numbers it also provides the statistical conclusion in the white-background box, “The value of the statistic is greater than 6.635. This indicates that there is a less than 1 percent chance that these results would have been obtained absent any form of bias. Therefore, you may conclude that these results may have been the result of bias.” That last sentence is hugely significant. If you want to know a little bit more about Chi Square analysis, check out the material from the folks at

Step 8 – The next number is probably the most significant for any formal analysis, namely, the Standard Deviation report. This is the number that the courts prefer to work with the most.  It simply measures how far the distribution of awards was for women from what would normally be expected in this particular workforce.  Simply put, if there are more than two standard deviations of difference between the rate men received awards and the rate at which women got them, then an arbitrator, EEOC or a judge is permitted to decide that the difference is due to illegal discrimination.  As you can see in the report, there were -4 standard deviations.  If you filed a grievance alleging illegal gender discrimination based on these facts as well as a violation of a contract requirement such as that awards are to be distributed “fairly and equitably,” the arbitrator would be within his/her rights to conclude these numbers show violations of both or perhaps just the contract standard. In either case, the union wins. Try Yahoo’s explanation of standard deviation if you want to know a little more about it.

Let’s stop here and ignore the rest of the report for now. Even though only two out of the three statistical tests uncovered adverse impact, the two more sophisticated tests support show that there is.

Step 9 – If the calculator’s numbers point to an improper disparity hitting one or more classes, you have options. One course of action would be to file a grievance asking that a greater percentage of women be given awards retroactively and that the system be corrected going forward. But, we do not want to mislead you. There are several other legal hurdles to clear if you are alleging illegal discrimination and we strongly recommend that you get a labor/employment lawyer involved to help you through them. There are things to know about sample size, similarly situated employees, adverse personnel actions, the criteria for awards, etc.

A second option you have is to use this information at the bargaining table to demand improvements to the award process. Section 3 of the Uniform Guidelines on Employee Selection Procedures demands that where there is adverse impact that look for a way to change how it makes the decision in question.

A third option is to put the information out to employees and ask them to contact the union with whatever personal observations or stories they have suggesting that something is very wrong with how managers decide who gets awards.  At times statistics with a few good examples of individual unexplainable decisions can greatly strengthen a case.

Step 10 – Do a little more reading before you jump into this effort with both feet.  An arbitrator issued an extremely well-written opinion on an NTEU grievance claiming discrimination on the distribution of bonuses.  Check it out. Another interesting case to read is known at Gilbert M. Jefferson et. al v. Michael J. Astrue, Social Security Administration EEOC No. 0120081816 (4/28/11)




About AdminUN

FEDSMILL staff has over 40 years of federal sector labor relations experience on the union as well as management side of the table and even some time as a neutral.
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