
667 F.Supp. 6 (1987)
Clyde J. ARNOLD, Jr., et al., Plaintiffs,
v.
POSTMASTER GENERAL, Defendant.
Charles Ray NETHERTON, et al., Plaintiffs,
v.
POSTMASTER GENERAL, Defendant.
Civ. A. Nos. 85-2571, 86-2291.
United States District Court, District of Columbia.
August 13, 1987.
As Amended August 20 and November 10, 1987.
*7 *8 Joseph E. Kolick, Jr. and Cyril V. Smith of Dickstein, Shapiro & Morin, Washington, D.C., for plaintiffs.
Stuart H. Newberger, Asst. U.S. Atty., Anthony W. DuComb, Sr. Atty., and Diana E. Johnson of the U.S. Postal Service, Office of Labor Law, Washington, D.C., for defendant.
CHARLES R. RICHEY, District Judge.


                      TABLE OF CONTENTS
I.   INTRODUCTION AND BACKGROUND                                         9
     A. The United States Postal Inspection Service                            10
     B. The United States Postal Inspection Service's Career Path
     Policy                                                             11
II.  PROCEDURAL HISTORY                                                 12
III. PROCEDURAL RULINGS                                                 13
     A. Class Certification Is Appropriate Under Rule 23(b)(2) and
     Local Rule 203.                                                    13
         1. Both Parties Sought Class Certification.                    13
         2. By Consent, the Parties Agreed to Tentative Class Certification
         Under Rule 23(b)(2) to Include Postal Inspectors Affected
         by the Career Path Policy.                              14
         3. Plaintiffs Only Challenge the Senior-First Rule of the
         Career Path Policy; Therefore, the Court Will Redefine the
         Class to Comprise Only Postal Inspectors Affected by the Senior-First
         Rule Because Only They Have Standing to Challenge
         the Rule.                                                14
         4. Rule 23 Applies to Class Actions Against the Federal
         Government, Rather Than the ADEA's Opt-In Requirement
         Applicable to Private Employers.                               15
         5. Class Certification Is Appropriate Under Rule 23 and Local
         Rule 203.                                                      15
     B. Although Most of the Named Plaintiffs Met the ADEA's Notice
     Requirements, Defendant's Motion to Dismiss Brady and Rittiner
     as Class Representatives Must be Granted Because They
     Did Not Satisfy the Notice Requirements; Brady and Rittiner
     May, However, be Eligible for Relief as Members of the Protected
     Class and, Therefore, Defendant's Motion to Dismiss Brady and
     Rittiner as Class Members Is Denied.                               16
     C. All of the Named Plaintiffs Have Standing to Challenge the
     Senor-First Rule as a Violation of the ADEA.                       17
IV.  WHEN PLAINTIFFS "ACCEPTED" TRANSFERS UNDER THE
     CPP, THEY DID NOT WAIVE THEIR RIGHTS TO CHALLENGE
     THE SENIOR-FIRST RULE AS A VIOLATION OF THE ADEA.                  18
V.   THE SENIOR-FIRST RULE OF THE CAREER PATH POLICY
     VIOLATES THE AGE DISCRIMINATION IN EMPLOYMENT ACT
     UNDER BOTH A THEORY OF DISPARATE IMPACT AND DISPARATE
     TREATMENT.                                                  18
     A. The Senior-First Rule Has A DISPARATE IMPACT on Postal
     Inspectors 40 Years of Age and Older.                              19
         1. The Plaintiffs Have Established That the Senior-First
         Rule Falls More Harshly on Postal Inspectors 40 Years of
         Age and Over.                                                  19
             a. The Senior-First Rule Is a Discriminatory Employment
             Policy.                                               19
             b. Defendant's Senior-First Rule Has a Statistically Significant
             DISPARATE IMPACT on Plaintiffs.                   20
                 i. The Relevant Time Period Is From December 1,
                 1980 to September 1, 1985.                             20



*9
      ii. The Effect of the Senior-First Rule Is Most Accurately
      Reflected by Plaintiffs' Statistics.                20
      iii. The Statistics Establishing DISPARATE IMPACT.         22
2. No Valid Business Necessity Justifies the Senior-First
Rule.                                                            23
3. Even if Defendant Had a Business Necessity to Transfer
the Most Senior Level 23 Postal Inspectors, a Non-Discriminatory
Alternative Was Available.                                25
B. The Senior-First Rule Constitutes DISPARATE TREATMENT
of Plaintiffs Because Defendant's Use the Rule as a Pretext to
Discriminate Against Plaintiffs Because of Their Age.            26
    1. Plaintiffs' Statistical and Antedotal Evidence Raises an
    Inference of Discrimination Against Postal Inspectors 40
    Years of Age and Over Because of Their Age.                  27
    2. Defendant Has Not Sustained Its Burden of Persuading
    Producing Evidence of a Legitimate, Non-Discriminatory
    Business Reason for the Senior-First Rule.                   27
    3. Plaintiffs' Have Proven by a Preponderance of the Evidence
    That Defendant's Reason for the Senior-First Rule Was
    But a Pretext for Its Discriminatory Animus.                 27
    4. Defendant Knew the Senior-First Rule Violated the
    ADEA and, Therefore, Defendant's Conduct Was Willful.        28
VI. CONCLUSION                                                   28


I. INTRODUCTION AND BACKGROUND[1]
This class action arises out of plaintiffs' challenge to the senior-first rule ("Rule") of the United States Postal Service's Career Path Policy ("CPP" or "Policy"). Pursuant to the senior-first rule, the Postal Service directs the most senior and oldest level 23 postal inspectors from the cities, towns and hamlets across the land to transfer to New York City and thirteen other major metropolitan areas.[2] Directing the most senior level 23 postal inspectors to transfer to major metropolitan areas adversely affects the older postal inspectors because the cost of living and housing in New York City and the other thirteen major metropolitan areas is significantly higher than in non-major metropolitan areas. Defendant knew that the Age Discrimination in Employment Act ("ADEA"), 29 U.S.C. §§ 621-634, prohibits them from implementing policies, such as the Career Path Policy and its senior-first rule, that discriminate against persons because of their age. Nevertheless, defendant began to systematically transfer the most senior and oldest level 23 postal inspectors to major metropolitan areas on December 1, 1980.
Plaintiffs successfully advance two theories in support of their claim that the senior-first rule violates the ADEA. First, plaintiffs establish that the senior-first rule had a disparate impact on postal inspectors 40 years of age and older. In its defense, defendant unpersuasively argues that the senior-first rule was implemented out of an alleged business necessity to alleviate the shortage of experienced postal inspectors in major metropolitan areas. Plaintiffs convincingly rebut defendant's alleged business necessity defense correctly arguing that defendant's need for experienced postal inspectors could be met by using a non-discriminatory random system.
Plaintiffs' second claim is that the senior-first rule results in the disparate treatment of postal inspectors 40 years of age and above. Plaintiffs' statistical and antedotal testimony clearly raises an inference of discrimination on the basis of age. Defendant fails to proffer a legitimate, nondiscriminatory *10 business reason for reassigning the most senior and older level 23 postal inspectors to the largest and most expensive cities. But, even if defendant's reason was legitimate and nondiscriminatory, plaintiffs proved that defendant's reason was a pretext to hide its discriminatory animus toward older postal inspectors.
In addition to specifically addressing plaintiffs' two theories of disparate impact and disparate treatment, defendant contends that some of the plaintiffs' waived their rights to challenge the senior-first rule under the ADEA when they were arbitrarily transferred under the Career Path Policy. Defendant says that these plaintiffs waived their rights by agreement. Plaintiffs properly assert that no such agreement was made and even if an agreement was made, it is void and unenforceable.
Finally, defendant moves to dismiss plaintiffs Brady and Rittiner for failing to comply with the ADEA's notice requirements.
By Order of this Court, the trial was bifurcated into a liability phase and a remedy phase. On May 20-22, 1987, the Court heard the liability phase of this case. Upon thorough consideration of the record, including the testimony, the exhibits, and the Court's judgment as to the credibility of the witnesses herein, the Court certifies this case as a Rule 23(b)(2) class action, grants defendant's motion to dismiss plaintiffs Brady and Rittiner as class representatives, but denies defendant's motion to dismiss Brady and Rittiner as class members, and finds that the plaintiffs did not waive their rights under the ADEA when they were transferred pursuant to the senior-first rule. More importantly, the Court finds that plaintiffs have proved that the senior-first rule violates the ADEA under both a theory of disparate impact and disparate treatment. Accordingly, the Court will issue an order of even date herewith consistent with the Opinion herein.

A. The United States Postal Inspection Service

There are approximately 1900 postal inspectors located in the United States and Puerto Rico responsible for protecting the United States mail, postal employees and mail system. These postal inspectors are part of the Postal Inspection Service, which is the law enforcement and audit arm of the United States Postal Service. See 39 U.S.C. §§ 404(a)(7) & 2008(d). Incident to its power to investigate criminal offenses, the Postal Inspection Service is charged with enforcing approximately 65 separate statutory sections of the United States Code. See Defendant's Exhibit ("DX") 3.
The Postal Inspection Service is administered by the Chief Postal Inspector, who reports directly to the Postmaster General. From 1979 through 1985, Kenneth Fletcher was Chief Postal Inspector until replaced by Charles Clauson, who holds the position today. Reporting to the Chief Postal Inspector are Assistant Chief Postal Inspectors, who oversee Regional Chief Postal Inspectors. Each region is comprised of Divisions headed by an Inspector-in-Charge. In 1982, the 17 Divisions were reorganized to form 39 Divisions. Each division is further divided into domiciles.
Except for the period between 1970 and 1984, postal inspectors have been recruited from within the Postal Service, and after 1984 have been required to have a college degree. See DX 7. Postal Inspection Service regulations require postal inspectors to relocate when lawfully and legitimately dictated by the needs of the Service. See DX 10. To be hired, each postal inspector must state that he or she is willing to relocate pursuant to a lawful policy to anyplace in the continental United States, Puerto Rico, Alaska and Hawaii. See DX 7 & 11A-2. Importantly, these relocation requirements do not mention the Age Discrimination in Employment Act or that a transfer policy, such as the senior-first rule, must comply with the ADEA, or that signing such statements constitutes a waiver of any rights under the ADEA. See id.
After 11 weeks of training in Potomac, Maryland, see DX 7, postal inspectors spend one year as a level 17 postal inspector. They then spend one year at level 19 and two years at level 21 before being *11 promoted to level 23.[3] The primary difference between level 21 and level 23 does not stem from familiarity with the various tasks postal inspectors perform, but from the procedure by which postal inspectors are assigned work. Level 21 postal inspectors receive miscellaneous assignments spanning four functional areas, which include fraud and prohibited mailings, audit, external crimes (crimes committed against the Postal Service by non-employees), and internal crimes (crimes committed against the Postal Service by employees). Thus, level 21 postal inspectors are familiar with all four functional areas. Level 23 postal inspectors, however, specialize in one functional area, and receive assignments only in that one area.

B. The United States Postal Inspection Service's Career Path Policy

In response to a shortage of experienced postal inspectors in the fourteen major metropolitan areas, particularly New York City, the United States Postal Inspection Service instituted the Career Path Policy on December 1, 1980. See Plaintiffs' Exhibit ("PX") 16. The Policy has three means of effecting five year reassignments to major metropolitan areas  voluntary level 23 lateral reassignments, voluntary level 21 lateral reassignments and involuntary directed transfers of the most senior level 23s in the nation. See PX 16. Plaintiffs challenge only this latter component of the Policy otherwise known as the senior-first rule because it transfers the older postal inspectors first. To fully understand why the senior-first rule violates the ADEA and why defendant does not have a legitimate need for the senior-first rule it is necessary to consider the aspects of the Career Path Policy not challenged by plaintiffs.
The first aspect of the Policy not challenged here is the voluntary level 23 lateral reassignment. A voluntary level 23 lateral reassignment occurs when a level 23 postal inspector volunteers to serve five years in a major metropolitan area with a vacancy. If more than one level 23 postal inspector bids on a given vacancy, the postal inspector who bid for the vacancy first is awarded the lateral reassignment, regardless of the relative seniority of the competing bidders. See PX 16.
The second aspect of the Career Path Policy which is not challenged is that permitting voluntary level 21 lateral reassignments. If a vacancy is not filled by a voluntary level 23 lateral reassignment, the Postal Inspection Service advertises the vacancy among level 21 postal inspectors. Level 21 postal inspectors may then volunteer for a lateral reassignment as a level 21 postal inspector or bid on a level 23 vacancy. See Defendant's Proposed Findings of Fact ("DF") ¶ 38. When more than one level 21 postal inspector bids on a level 23 vacancy, the most qualified bidder is reassigned. See PX 16.
The third aspect of the Career Path Policy that is being challenged here can be described as follows. If a vacancy is not filled by a voluntary level 21 or level 23 lateral reassignment, the Postal Inspection Service directs the most senior eligible level 23 postal inspector in the nation to serve five years in the major metropolitan area with the vacancy. See PX 16. Although level 23 postal inspectors specialize in one of four functional areas, the senior postal inspector's area of expertise is not considered when directing transfers. Seniority is the sole consideration in the directed transfers under attack in the case herein. As indicated, plaintiffs challenge this senior-first rule of the directed transfer component of the Policy.
The Career Path Policy has certain exemptions which are also not challenged here. These exemptions are relevant because they determine whether a postal inspector is subject to the senior-first rule. Whether a postal inspector is eligible to receive a directed transfer depends on whether he or she appears on the directed *12 transfer list of level 23 postal inspectors or is exempt from that list. All level 23 postal inspectors are ranked on the directed transfer list in order from the most senior to the least senior with the following exceptions: 1) postal inspectors within five years of retirement eligibility are permanently exempt; 2) postal inspectors appointed before December 15, 1980 are permanently exempt (this would have exempted all 39 named plaintiffs but for the fact that this exemption was not created until September 23, 1985, after this litigation began); 3) postal inspectors who have physically relocated to a new residence as a result of an official reassignment or promotion are temporarily exempt for two years, and if reassigned to Hawaii, Alaska, or Puerto Rico, are temporarily exempt for three years; 4) postal inspectors currently assigned to major metropolitan areas are temporarily exempt as long as they are assigned to the major metropolitan area; and 5) postal inspectors who have served five years in a major metropolitan area at level 23 or level 24 are permanently exempt. See PX 16. As postal inspectors become exempt or their temporary exemptions expire, the composition of the pool of postal inspectors eligible for directed transfers changes. Consequently, the exemptions cause a particular postal inspector's rank on the directed transfer list to change from day to day.

II. PROCEDURAL HISTORY
Three groups of plaintiffs filed requests for administrative relief with defendant and later with the Equal Employment Opportunity Commission ("EEOC"). The Court will describe those three groups and their status. This description is set forth so that the chronology of this case can be understood, but the net effect is that all three groups are part of the certified class in this case.
Almost two years after the implementation of the Career Path Policy in December of 1980, Charles Netherton filed a class action on behalf of himself and other similarly situated Postal Inspectors in the United States District Court for the Middle District of Florida. See Netherton v. United States Postal Service, Civil Action 82-504-ORL-CIV-R (filed Sept. 28, 1982 M.D. Fla.). Upon filing the lawsuit, Mr. Netherton moved for a temporary restraining order to enjoin the Postal Service from directing him to transfer to New York City. On October 1, 1982, Mr. Netherton's motion was denied in that court. Subsequently, defendant filed a motion to dismiss or for summary judgment, which on June 17, 1983, was also denied. The Netherton case was then stayed pending the conclusion of plaintiffs' administrative proceedings before the Equal Employment Opportunity Commission ("EEOC").
In July of 1983 the complaints examiner issued a decision in the Netherton case recommending that the Career Path Policy violated the ADEA. On August 30, 1983, the Postal Service rejected the recommendation of the complaints examiner and found that the Policy did not violate the ADEA. A motion to lift the stay was filed by defendant on September 6, 1983 and denied on October 12, 1983. On September 20, 1983, the Netherton plaintiffs filed a consolidated appeal with the EEOC of the Postal Service's final decision.
On March 25, 1985, the EEOC dismissed the Netherton plaintiffs' appeals because the United States District Court for the Middle District of Florida had retained jurisdiction over their claims. Defendant then moved to dismiss the second group of plaintiffs' appeals to the EEOC. Defendant's motion is still pending before the EEOC. Cf. Grubbs v. Butz, 514 F.2d 1323 (D.C.Cir. 1975) (any action taken pursuant to a regulation is independent of an employee's right to file a civil action and can be simultaneous with the civil action).
During this time, postal inspectors Arnold, Bell, D. Brown, Garland, LeBlanc, Nelson and Syverson filed administrative complaints challenging the senior-first rule as a violation of the ADEA. In September of 1984, the complaints examiner again issued a recommended decision that the Policy violated the ADEA. Again, the Postal Service rejected the complaints examiner's recommendation. On October 29, 1984, this second group of postal inspectors appealed *13 the Postal Service's final decision to the EEOC. That appeal is still lying dormant before the EEOC. Cf. Grubbs v. Butz, 514 F.2d 1323 (D.C.Cir.1975) (any action taken pursuant to a regulation is independent of an employee's right to file a civil action and can be simultaneous with the civil action).
Meanwhile, a third group of plaintiffs, Bottita, R. Brown, Hill, Hoffman, Hurlbut, Jones, Kamm, Kennerson, Lingle, Manning, Martinez, McClelland, Parkinson, Post, Reinardy, Scott and Thompson, also filed administrative complaints contesting the senior-first rule on the ground that it violates the ADEA. In a decision dated May 20, 1985, the Postal Service cancelled the Administrative complaints of this third group of plaintiffs. These plaintiffs' subsequent appeals to the EEOC are also still pending. Cf. Grubbs v. Butz, 514 F.2d 1323 (D.C.Cir.1975) (any action taken pursuant to a regulation is independent of an employee's right to file a civil action and can be simultaneous with the civil action).
On June 11, 1985, the Netherton plaintiffs moved the United States District Court for the Middle District of Florida to dismiss their case without prejudice. Defendant opposed plaintiffs' motion and moved to lift the stay. On June 25, 1985, plaintiffs' motion to dismiss was denied and defendant's motion to lift the stay was granted. On or about September 4, 1985, defendant moved the United States District Court for the Middle District of Florida to certify the Netherton case as a class action. That motion remained pending until the parties consented to a conditional class certification at the May 18, 1987 pretrial conference before this Court.
On August 13, 1985, the second and third groups of plaintiffs filed suit in the United States District Court for the District of Columbia. See Arnold v. United States Postal Service, 649 F.Supp. 676 (D.D.C.). Four additional plaintiffs joined the second and third groups of plaintiffs in the Arnold lawsuit  Rittiner, Brady, Jas and Cyryt. Defendant's motion to dismiss plaintiffs Brady and Rittiner as class representatives is addressed herein.
Six days after the Arnold case was filed, the Netherton plaintiffs moved to transfer the Netherton case from the United States District Court for the Middle District of Florida to the United States District Court for the District of Columbia. By Order dated August 8, 1986 the Netherton case was transferred, and on September 16, 1986, the Netherton and Arnold cases were consolidated by consent of the parties pursuant to Federal Rule of Civil Procedure 42(a).
After the Netherton and Arnold cases were consolidated, cross motions for summary judgment and defendant's motion to strike all of plaintiffs' requests for damages other than backpay were considered. In an Opinion dated December 9, 1986, this Court denied the cross motions for summary judgment because there were genuine issues of material fact as to whether the senior-first rule constituted disparate treatment of plaintiffs on the basis of age and whether the senior-first rule had a disparate impact on postal inspectors 40 years of age and above. See Arnold v. United States Postal Service, 649 F.Supp. 676 (D.D.C.1986).
Upon consideration of defendant's motion to strike plaintiffs' request for all relief beyond backpay, the Court denied, without prejudice, defendant's motion to strike, reserving final judgment on remedies until and if the Court finds defendant liable. See id. at 684. Consistent with the order denying defendant's motion to strike, by Order of April 28, 1987, the Court bifurcated the liability and remedy stages of the trial.

III. PROCEDURAL RULINGS

A. Class Certification Is Appropriate Under Rule 23(b)(2) and Local Rule 203.


1. Both Parties Sought Class Certification.

Whether class certification is appropriate in this case has been an issue from the day Mr. Netherton filed the first of these consolidated cases. See Complaint, Netherton v. United States Postal Service, Civil Action *14 82-504-ORL-CIV-R (filed Sept. 28, 1982 M.D.Fla.). In his complaint, Mr. Netherton purported to represent a class
comprised of a group of persons who are or who have been senior level 23 non-exempt Postal Inspectors, age 40 and above, who have been, are being, or may be adversely affected by the forced transfer provisions of the Inspector Career Path Policy. The class includes all Postal Inspectors presently on the seniority list of non-exempt Level 23 Postal Inspectors used by the Chief Inspector for the purpose of making forced transfers under the policy.... It includes those Level 23 Postal Inspectors above the age of 40 who have only a temporary exemption to the policy. The class further includes the senior non-exempt Level 23 Postal Inspectors who have been previously injured under the policy or who have preserved their right to obtain relief by the previous filing or attempted filing of individual complaints of Age Discrimination.
Id. at 2-3, ¶ 5. On or about September 4, 1985, the issue of class certification was against raised, but this time by defendant. Defendant moved the United States District Court for the Middle District of Florida to certify the following class pursuant to Rule 23 of the Federal Rules of Civil Procedure:
Present, former, or future Postal Inspectors who have, or will have, timely filed administrative complaints pursuant to 29 C.F.R. Part 1613 asserting that the Postal Inspection Service Career Path Policy adversely impacted them by causing their transfer or resignation from the Inspection Service when they were 40 years of age or older in violation of the Age Discrimination in Employment Act, 29 U.S.C. § 633a.
Motion for Certification, Netherton v. United States Postal Service, Civil Action 82-504-ORL-CIV-R (filed Sept. 4, 1985 M.D.Fla.). When the Netherton case was transferred to this Court on August 8, 1986, the United States District Court for the Middle District of Florida had not decided either plaintiffs' or defendant's requests for class certification. Accordingly, this Court inherited the class certification issue.

2. By Consent, the Parties Agreed to Tentative Class Certification Under Rule 23(b)(2) to Include Postal Inspectors Affected by the Career Path Policy.

At the May 18, 1987 pre-trial conference, upon consent of the parties, the Court granted defendant's motion for class certification under Rule 23(b)(2). By oral stipulation, the parties defined the class to include
All postal inspectors of the United States Postal Service between December 1, 1980 and September 1, 1985 who were, are, or have been affected by the Career Path Policy.

3. Plaintiffs Only Challenge the Senior-First Rule of the Career Path Policy; Therefore, the Court Will Redefine the Class to Comprise Only Postal Inspectors Affected by the Senior-First Rule Because Only They Have Standing to Challenge the Rule.

Notwithstanding that the class was tentatively certified upon consent of the parties to include postal inspectors affected by the "Career Path Policy," plaintiffs only challenge the senior-first rule of that Policy. To join the class each class member must have standing to challenge the senior-first rule. See Foster v. Center Township of LaPorte County, 798 F.2d 237, 244 (7th Cir.1986); Slaughter v. Levine, 598 F.Supp. 1035, 1041 (D.Minn.1984), aff'd in part and rev'd on other grounds, 801 F.2d 288 (8th Cir.1986) (citing Lamb v. Hamblin, 57 F.R.D. 58, 60-61 (D.Minn.1972); Metropolitan Area Housing Alliance v. United States Department of Housing and Urban Development, 69 F.R.D. 633, 633 (D.Ill.1976)); McElhaney v. Eli Lilly & Co., 93 F.R.D. 875, 878 (D.S.D.1982).
The tentative class comprising postal inspectors affected by the Career Path Policy is overbroad in that it includes postal inspectors affected by parts of the Career Path Policy beyond the senior-first rule, such as the voluntary level 21 and 23 lateral reassignment provisions. Because postal inspectors not injured by the senior-first rule do not have standing to challenge that *15 rule, the Court will exercise its authority to limit the class to include only postal inspectors who have been affected by the senior-first rule. See Sears v. Atchison, Topeka & Santa Fe Railway, 749 F.2d 1451, 1456 (10th Cir.1984); Slaughter, 598 F.Supp. at 1041; Graham v. Heckler, 573 F.Supp. 1573, 1581 (N.D.W.Va.1983); Lamb, 57 F.R.D. at 60-61; Metropolitan Area Housing Alliance, 69 F.R.D. at 633. Those with standing include senior postal inspectors who because of the senior-first rule were directed to transfer, resigned to avoid a directed transfer, or volunteered for lateral reassignment to avoid a directed transfer, or others adversely affected by the senior-first rule. Accordingly, the Court redefines the class to include the following postal inspectors:
All postal inspectors of the United States Postal Service between December 1, 1980 and September 1, 1985 who were, are, or have been affected by the senior-first rule of the Career Path Policy.

4. Rule 23 Applies to Class Actions Against the Federal Government, Rather Than the ADEA's Opt-In Requirement Applicable to Private Employers.

Discrimination on the basis of age is prohibited by two distinct sections of the ADEA  section 623(a)(1) prohibits discrimination by private employers and section 633a(a) prohibits discrimination by federal employers. On April 6, 1978, the section prohibiting age discrimination by federal employers was amended as follows:
Any personnel action of any department, agency, or other entity referred to in subsection [633a(a)] shall not be subject to, or affected by, any provision of the [ADEA], other than the provisions of [subsection 631(b) ] and the provisions of [section 633a].
29 U.S.C. § 633a(f).
Prior to the 1978 amendment, ADEA actions against employers were "enforced in accordance with the powers, remedies, and procedures ... of the Fair Labor Standards Act ["FLSA"]," 29 U.S.C. § 626(b), which has an affirmative opt-in requirement for class actions: no person may become a plaintiff "unless he gives his consent in writing to become such a party." 29 U.S.C. § 216. This opt-in requirement is incorporated through section 626(b) of the ADEA and is mutually exclusive with Rule 23.
Since the 1978 amendment, providing that only subsection 631(b) and section 633a of the ADEA apply to federal employers, the FLSA's affirmative opt-in requirement for class actions does not apply to federal employees. See Moysey v. Andrus, 481 F.Supp. 850 (D.D.C.1979), appeal withdrawn, U.S.C.A. No. 80-2174 (D.C.Cir. Sept. 25, 1980). Accordingly, this Court in Moysey certified the class under Rule 23(b)(1)(B) and 23(b)(2). Id. at 854-55; see also Christie v. Marston, 19 FEP 87 (N.D. Ill.1979) (Rule 23 class action against Federal Home Loan Bank Board). Class certification under Rule 23 is similarly appropriate in this case.

5. Class Certification Is Appropriate Under Rule 23 and Local Rule 203.

Rule 23(a) and Local Rule 203 of this Court permit class certification only if (1) the class is so numerous as to make joinder impracticable, (2) there are common questions of law and fact, (3) the claims of the representative parties are typical of the class, and (4) the representative parties will fairly and adequately protect the interests of the class. See Fed.R.Civ.P. 23(a); Local Rule 203.
The Court can be certain that the class will include no less than the 39 plaintiffs named in the Netherton and Arnold complaints and may, based on defendant's representation, encompass as many as several hundred plaintiffs. In that joinder would be impracticable with a class of 39 to a few hundred plaintiffs, the numerosity requirement of Rule 23(a)(1) is satisfied.
As defendant's motion for class certification suggests and the complaints herein allege, all plaintiffs challenge the senior-first rule of the Career Path Policy on the ground that it violates the Age Discrimination in Employment Act. Accordingly, there are common questions of law and fact as required by Rule 23(a)(2).
Thirty-nine plaintiffs are named in the two complaints. Each of these representative *16 plaintiffs claims to have been affected by the senior-first rule and challenges the Rule under the ADEA. The class these plaintiffs represent comprises all postal inspectors affected by the senior-first rule. Thus, the Court finds that Rule 23(a)(3)'s prerequisite that the claims of the representative parties be typical is satisfied.
Rule 23(a)(4) requires the representative parties to fairly and adequately protect the interests of the class. This requirement has two components. First, the representatives' interests must not be antagonistic to the interests of the class. This is not the case here, as the representatives and the class both want the Court to find that the senior-first rule violates the ADEA. Secondly, class counsel must be diligent and competent. That class counsel satisfies this requirement is borne out by the record. Thus, Rule 23(a)(4) is met.
Finally, Rule 23(b)(2) permits class certification only if the party opposing the class has acted against the whole class, making injunctive or declaratory relief against the defendant appropriate for the class as a whole. See Fed.R.Civ.P. 23(b)(2). At issue here is a rule that, by operation, applies to all senior postal inspectors unless specifically exempted. Because defendant has acted against the protected class as a whole, certification under Rule 23(b)(2) is appropriate. Therefore, in accordance with Federal Rule of Civil Procedure 23 and Local Rule 203, the Court finds that a Rule 23(b)(2) class action is appropriate and proper in this case.

B. Although Most of the Named Plaintiffs Met the ADEA's Notice Requirements, Defendant's Motion to Dismiss Brady and Rittiner as Class Representatives Must be Granted Because They Did Not Satisfy the Notice Requirements; Brady and Rittiner May, However, be Eligible for Relief as Members of the Protected Class and, Therefore, Defendant's Motion to Dismiss Brady and Rittiner as Class Members Is Denied.

To bring an ADEA action against a federal employer a federal employee must, within 180 days from the alleged discriminatory act, give the EEOC a 30 day notice of an intention to sue. See 29 U.S.C. § 633a(d); McKinney v. Dole, 765 F.2d 1129, 1140-41 (D.C.1985); Macellaro v. Goldman, 643 F.2d 813 (D.C.Cir.1980). Alternatively, a federal employee may choose to file a complaint with the EEOC. See 29 U.S.C. § 633a(d); Dodson v. United States Army Finance and Accounting Center, 636 F.Supp. 894, 896 (S.D.Ind.1986).
Defendant concedes that each of the plaintiffs filed a timely administrative complaint challenging the senior-first rule as a violation of the ADEA, with the exception of plaintiffs Brady and Rittiner. Mr. Brady was ordered to transfer on October 5, 1983 and transferred on January 9, 1984. Rather than file a notice of intent to sue, Mr. Brady filed an administrative complaint on January 13, 1984. On May 3, 1984 the United States Postal Service rejected Mr. Brady's complaint because it was not timely filed. Mr. Brady did not appeal that action to the EEOC within 20 days or file a civil suit within 30 days as required by the applicable regulations. See 29 C.F.R. § 1613.281(a) (upon receipt of notice of final agency action on the complaint, the complaint may appeal to the EEOC within 20 days or file a civil action within 30 days). Accordingly, defendant's motion to dismiss Mr. Brady as a class representative must be granted with the caveat that plaintiff Brady may still obtain relief as a class member.
Mr. Rittiner was directed to transfer on September 3, 1981. He filed an administrative complaint and it was rejected on June 8, 1982. Mr. Rittiner also chose not to appeal the agency's decision to the EEOC within 20 days or to file a civil action within 30 days. See 29 C.F.R. § 1613.281(a) (upon receipt of notice of final agency action on the complaint, the complainant may appeal to the EEOC within 20 days or file a civil action within 30 days). Accordingly, defendant's motion to dismiss Mr. Rittiner as a class representative must be granted with the caveat that plaintiff Rittiner may still obtain relief as a class member.
*17 That plaintiffs Brady and Rittiner cannot remain named as class representatives does not preclude them from obtaining relief under the ADEA as class members in a Rule 23 class action. In an ADEA class action against a private employer, courts have held that consenting class members need not individually comply with the charge-filing requirements. See, e.g., Mistretta v. Sandia Corp., 639 F.2d 588, 593-95 & n. 3 (10th Cir.1980); Bean v. Crocker National Bank, 600 F.2d 754, 759 (9th Cir.1979); Russell v. Curtin Matheson Scientific, Inc., 17 FEP 845, 848 (S.D.Tex.), app. den., 18 FEP Cas 866 (5th Cir.), cert. denied, 439 U.S. 972, 99 S.Ct. 466, 58 L.Ed.2d 432 (1978). Similarly, under Title VII, where class actions are maintained under Rule 23, only the named plaintiff need satisfy the charge-filing requirements. See, e.g., Inda v. United Airlines, 565 F.2d 554, 559 (9th Cir.1977), cert. denied, 435 U.S. 1007, 98 S.Ct. 1877, 56 L.Ed.2d 388 (1978); Wetzel v. Liberty Mutual Insurance Co., 508 F.2d 239, 246 (3rd Cir.), cert. denied, 421 U.S. 1011, 95 S.Ct. 2415, 44 L.Ed.2d 679 (1975). Therefore, since this case is a Rule 23 class action under the ADEA, the Court concludes that plaintiffs Brady and Rittiner are entitled to relief as class members if they were employed by the United States Postal Service between December 1, 1980 and September 1, 1985 and affected by the senior-first rule of the Career Path Policy.

C. All of the Named Plaintiffs Have Standing to Challenge the Senior-First Rule.

The ADEA prohibits "all [discriminatory] personnel actions affecting employees ... who are at least 40 years of age," 29 U.S.C. § 633a(a) (emphasis added), and gives standing to sue to all "aggrieved persons." 29 U.S.C. § 633a(c). All 39 named plaintiffs were at least 40 years of age when they were adversely affected by the Career Path Policy. Each was ranked on the directed transfer list, placing them in imminent jeopardy of being directed to transfer. Except for Albert Brady, all the named plaintiffs were at least 40 years of age when they were affected, see 29 U.S.C. § 633a(c) (aggrieved persons may sue), or injured, see, e.g., Synar v. United States, 626 F.Supp. 1374, 1380 (D.D.C.1986) (actual or threatened injury necessary for standing), by the senior-first rule because they received orders directing them to transfer to a major metropolitan area, or resigned or volunteered for a lateral reassignment to avoid a directed transfer. See PX 2-15, 51 & 52.
Plaintiffs Arnold, Brady, R.G. Brown, Caldwell, Day, DeFord, Erwin, Garland, Gholson, Hermanson, Hill, Hoffman, Jas, Jones, LeBlanc, Lingle, Manning, Martinez, Nelson, Netherton, Post, Reed, Rittiner, Scott, Syverson, and Tangney received directed transfers to major metropolitan areas when they were 40 years of age and above. See PX 51 & 52. Therefore, they were 40 years of age and older when they were adversely affected by the Policy.
Plaintiffs Bell, D.E. Brown, Bye, Kamm, Parkinson, Reinardy, and Thompson resigned when they were 40 years of age or older to avoid a directed transfer. Each of these plaintiffs was in imminent jeopardy of receiving a directed transfer because of their ranking on the seniority list. See PX 2-15, 44-50. All of these plaintiffs had family and financial restraints that compelled them to resign to avoid the adverse effects of a directed transfer.
When plaintiffs Bottita, Cyryt, Helmer, Hurlbut, Kenerson, and McClelland were 40 years of age and older, they were forced to volunteer for a lateral reassignment to an undesirable major metropolitan area to avoid a directed transfer to an even less desirable major metropolitan area. Each of the plaintiffs who volunteered for a lateral reassignment did so because they were approaching the point on the directed transfer seniority list where a directed transfer was imminent. See PX 2-15, 38-43. All of these plaintiffs had family and financial restraints that compelled them to volunteer for transfer to avoid the adverse effects of a directed transfer.
Albert Brady was 39 when he received a directed transfer to New York. Although Mr. Brady was not 40 years of *18 age when he was notified that he would be directed to transfer, he was 40 years of age when he was affected by a discriminatory personnel action, the senior-first rule. Mr. Brady was reassigned to New York City for five years from the day he reported for duty; he was 40 years old when he reported for duty. See PX 16 & 51. But for the Rule, Mr. Brady would not have been transferred and serving five years in New York City. Therefore, the Court finds that because Mr. Brady was affected by the senior-first rule when he was 40 years of age, he has standing to challenge that Rule. See 29 U.S.C. § 633a(c) (agrieved persons may sue), or injured; see also, Synar v. United States, 626 F.Supp. 1374, 1380 (D.D.C.1986) (actual or threatened injury necessary for standing).

IV. WHEN PLAINTIFFS "ACCEPTED" TRANSFERS UNDER THE CAREER PATH POLICY, THEY DID NOT WAIVE THEIR RIGHTS TO CHALLENGE THE SENIOR-FIRST RULE AS A VIOLATION OF THE ADEA.
Defendant's cross-examination of plaintiffs attempted to suggest that plaintiffs waived their rights to challenge transfers as a violation of the ADEA because plaintiffs knew that arbitrary transfers could be made at any time to any place when they became postal inspectors. While there is no question that plaintiffs knew they might be arbitrarily transferred, there is also no question that plaintiffs did not knowingly and voluntarily agree to be systematically transferred pursuant to a senior-first rule that unlawfully discriminated against them because of their age. Indeed, if defendant had transferred postal inspectors on a random basis, the disparate impact of the senior-first rule would have been avoided because a random system does not select the oldest postal inspector for transfer first.
That plaintiffs might be transferred at any time to any place to serve the needs of the Inspection Service is not a circumstance or fact which supports a factual or legal conclusion that it was a knowing and voluntary waiver of plaintiffs' prospective rights under the ADEA. See United States EEOC v. County of Calumet, 686 F.2d 1249, 1254 (7th Cir.1982) (employees do not waive rights under the ADEA where agreement does not expressly make reference to the ADEA or waive their rights under the ADEA). Even if it could be said that plaintiffs agreed to waive their rights by agreeing to transfer, such an agreement is void and unenforceable because it is contrary to public policy. See, e.g., Evans v. Jeff, 475 U.S. 717, 106 S.Ct. 1531, 89 L.E.d2d 747 (1986); Southland Corp. v. Keating, 465 U.S. 1, 104 S.Ct. 852, 79 L.Ed.2d 1 (1984); Restatement (Second) of Contracts sec. 178 (1981). Therefore, the Court finds that because defendant is prohibited by the ADEA from transferring plaintiffs pursuant to a policy that discriminates on the basis of age, plaintiffs may challenge the Rule as a violation of the ADEA.

V. THE SENIOR-FIRST RULE OF THE CAREER PATH POLICY VIOLATES THE AGE DISCRIMINATION IN EMPLOYMENT ACT BOTH UNDER A THEORY OF DISPARATE IMPACT AND DISPARATE TREATMENT.
Section 633a of the Age Discrimination in Employment Act ("ADEA"), which applies to federal employers, provides that
[a]ll personnel actions affecting employees ... who are at least 40 years of age ... in the United States Postal Service ... shall be made free from any discrimination based on age.
29 U.S.C. § 633a(a); see also 29 U.S.C. § 631(b) (protected class includes individuals at least 40 years of age). Plaintiffs advance two theories to prove that the senior-first rule discriminates against them based on age. First, plaintiffs contend that the senior-first rule has a disparate impact on postal inspectors 40 years of age and above. Plaintiffs' statistics establish that the adverse effects of the senior-first rule, which involuntarily transfers the oldest postal inspectors to cities with high costs of living, or causes them to resign or volunteer for lateral reassignment to avoid an involuntary transfer, falls more harshly on postal inspectors 40 years of age and older than on postal inspectors under 40 years of *19 age. Although defendant attempts to justify the senior-first rule by arguing that it has a business need for the most senior postal inspectors in the major metropolitan areas, the evidence before the Court clearly shows that defendant's real business need was for level 21 or higher postal inspectors of any seniority. Moreover, plaintiff convincingly proved that even if defendant's business need was for senior postal inspectors, that need could have easily been met by a nondiscriminatory, random transfer system.
Second, plaintiffs show that the senior-first rule constitutes disparate treatment because defendant knew that age and seniority were correlated when implementing the senior-first rule of the Career Path Policy and, therefore, intentionally subjected plaintiffs to disparate treatment because of their age by transferring them to cities with high costs of living. Defendant was unable to proffer a legitimate, nondiscriminatory reason for using the senior-first rule because no such reason exists. Indeed, plaintiffs have proved that defendant's alleged reason for the senior-first rule was pretextual and only served the purpose of masking defendant's unlawful motives. Therefore, upon consideration of all the evidence, the Court finds that Plaintiffs succeed on both theories.

A. The Senior-First Rule Has A DISPARATE IMPACT on Postal Inspectors 40 Years of Age and Older.

It is well settled that a violation of the ADEA may be proved by showing that an employment practice, such as the senior-first rule, which is involved in this case, has a disparate impact on a protected class, namely postal inspectors 40 years of age and above. See EEOC v. Borden's, Inc., 724 F.2d 1390, 1394-95 (9th Cir.1984); Leftwich v. Harris-Stowe State College, 702 F.2d 686, 690 (8th Cir.1983); Geller v. Markham, 635 F.2d 1027, 1032 (2d Cir. 1980), cert. denied, 451 U.S. 945, 101 S.Ct. 2028, 68 L.Ed.2d 332 (1981); Arnold v. United States Postal Service, 649 F.Supp. 676, 679-81 (D.D.C.1986); EEOC v. Westinghouse Electric Corp., 632 F.Supp. 343, 370 (E.D.Pa.1986); EEOC v. Governor Mifflin School District, 623 F.Supp. 734, 738-41 (E.D.Pa.1985); see also Schmid v. Frosch, 680 F.2d 248, 249-50 (D.C.Cir.1982) (implicitly approving a disparate impact theory); Allison v. Western Union Telegraph Co., 680 F.2d 1318, 1323 (11th Cir.1982) (same). To prove age discrimination under a disparate impact theory, plaintiffs need only establish that the senior-first rule disproportionately impacts, or falls more harshly on, postal inspectors 40 years of age and above. See Leftwich, 702 F.2d at 690; Geller, 635 F.2d at 1032. Such an impact is typically evidenced, as was presented in this case, by statistics from which discrimination may be inferred. See, e.g., Palmer v. Shultz, 815 F.2d 84, 91 n. 6 (D.C.Cir.1987) (statistical analysis must focus on appropriate source pool, which includes only those qualified for promotion, or in this case, those eligible for transfer); Segar v. Smith, 738 F.2d 1249, 1274 (1984) (same), cert. denied, 471 U.S. 1115, 105 S.Ct. 2357, 86 L.Ed.2d 258 (1985); Leftwich, 702 F.2d at 690; Geller, 635 F.2d at 1032. Moreover, unlike a disparate treatment case, plaintiffs need not prove discriminatory motive and animus in a disparate impact case. E.g., Leftwich, 702 F.2d at 690; Geller, 635 F.2d at 1032.

1. The Plaintiffs Have Established That the Senior-First Rule Is a Rule That Falls More Harshly on Postal Inspectors 40 Years of Age and Over.


a. The Senior-First Rule Is a Discriminatory Employment Policy.

Defendant argues in its post-trial brief that plaintiffs' disparate impact claim must fail because plaintiffs do not challenge an appropriate employment practice which disparately impacts them. See Defendant's Post-Trial Brief at 2-3 (filed June 9, 1987). Plaintiffs, however, have made it clear since this lawsuit was filed that they challenge the discriminatory senior-first rule of the Career Path Policy. See Complaint, Netherton v. United States Postal Service, Civil Action 82-504-ORL-CIV-R (filed Sept. 28, 1982 M.D.Fla.); Complaint, Arnold v. United States Postal Service, 649 *20 F.Supp. 676 (D.D.C.). It is defendant who has tried to mischaracterize plaintiffs' challenge to encompass the entire Career Path Policy in order to dilute the adverse impact that the senior-first rule has on plaintiffs. Plaintiffs have never challenged the aspects of the Policy permitting postal inspectors to volunteer for lateral reassignment.

b. Defendant's Senior-First Rule Has a Statistically Significant DISPARATE IMPACT on Plaintiffs.


i. The Relevant Time Period Is From December 1, 1980 to September 1, 1985.

Plaintiffs were subject to the senior-first rule from its implementation on December 1, 1980 until September 23, 1985 when the Postal Service exempted from directed transfers all those who were postal inspectors on December 1, 1980. See PX 16-E. By consent of the parties, the Court has certified a class comprising postal inspectors employed by the Postal Service between December 1, 1980 and September 1, 1985. This time frame was agreed to by counsel for the parties. Accordingly, the relevant time period for the purposes of analyzing the adverse effects of the senior-first rule on plaintiffs is from December 1, 1980 until September 1, 1985. See Palmer v. Shultz, 815 F.2d at 91 n. 6; Segar v. Smith, 738 F.2d at 1274.

ii. The Effect of the Senior-First Rule Is Most Accurately Reflected by Plaintiffs' Statistics.

Experts for both parties presented a multiplicity of statistics. Notwithstanding the statisticians' consensus as to the accuracy of each others arithmatical calculations, they reached opposite conclusions. This difference of opinion requires the Court to decide which statistics are appropriate. See Palmer v. Shultz, 815 F.2d at 91 n. 6; Segar v. Smith, 738 F.2d at 1274. For the reasons that follow the Court finds that plaintiffs' statistics best reflect the actual effect of the senior-first rule on plaintiffs.
First, plaintiffs' calculations analyze the effect of the senior-first rule on those to whom the rule applies, namely, eligible, or non-exempt, level 23 postal inspectors. In contrast, defendant analyzes the effect of the rule on all postal inspectors, including those who are temporarily or permanently exempt from the senior-first rule. It defies common sense to measure the effect of a policy, such as the senior-first rule, on persons to whom the rule does not apply, but the defendant's statistics did just this. See Palmer v. Shultz, 815 F.2d 84, 91 n. 6 (D.C.Cir.1987) (statistical analysis must focus on appropriate source pool, which includes only those qualified for promotion, or in this case, those eligible for transfer); Segar v. Smith, 738 F.2d 1249, 1274 (1984) (same), cert. denied, 471 U.S. 1115, 105 S.Ct. 2357, 86 L.Ed.2d 258 (1985). Therefore, the Court finds and accepts plaintiffs statistics as not only more credible but also because they are based on the appropriate source pool, which comprises only the postal inspectors eligible for a directed transfer during the relevant time period in this case.
Defendant's inclusion of exempt postal inspectors in its statistical analysis is also erroneous. Because the ADEA protects all persons 40 years of age and above, the senior-first rule's discriminatory transfers of some level 23 postal inspectors cannot be justified by its exemption of other level 23 postal inspectors. Therefore, a relevant statistical comparison looks at the effect of the senior-first rule only on the persons subjected to the Rule, which plaintiffs' witness did provide and which defendant's statistician did not provide. Indeed, this is what plaintiffs' statistics do, as they show the effect of the senior-first rule only on postal inspectors eligible for directed transfers pursuant to the Career Path Policy Rule in question in this case.
Another reason plaintiffs' statistics better reflect the effect of the senior-first rule is that they use "snap shot" data rather than "average" data. Snap shot data is better because in the instant case the average data does not accurately reflect the fluctuations in the pool of eligible postal inspectors which is reflected in the snap shot data. Because the exemptions caused the composition of the class of postal inspectors eligible for directed transfer to *21 change from day to day, the data that most accurately reflects the composition or age-mix of the class of postal inspectors subject to directed transfers is that data collected on or about the dates when directed transfers were actually made. See PX 52 (listing dates when directed transfers were ordered). Thus, plaintiffs' snap shot data best reflects the real and adverse effects of the senior-first rule on the protected class.
Defendant's use of average data[4] and the binomial distribution[5] is inappropriate because they do not accurately reflect the changing composition of the pool of postal inspectors eligible for directed transfer. An average is based on the premise that the pool of eligible postal inspectors is relatively stable, which was not the case here during the relevant period. See Cangelosi, Taylor and Rice, Basic Statistics, A Real World Approach at 30 (West 1979) (the disadvantage of the mean or average is that it will be overly influenced by extreme values). Such an assumption is inappropriate where the composition of the pool of postal inspectors eligible for directed transfer changes from day to day. Even Dr. Beckett, defendant's expert, admitted on cross examination that the averages he used did not reflect the actual number of postal inspectors 40 years of age and above located in non-major metropolitan areas.
Similarly, the use of the binomial distribution is invalid where the pool of eligible postal inspectors changes daily since a precondition for using the binomial distribution is that the probability of an event occurring remain constant, or in the instant case, that the age-mix of the pool of eligible postal inspectors remain constant. Here the number of postal inspectors 40 years of age and greater eligible for directed transfers changes daily. Therefore, the use of average data and the binomial distribution is improper in these circumstances. See Cangelosi, Taylor and Rice, Basic Statistics, A Real World Approach at 30 (West 1979).
That the use of snap shot data is more appropriate than average data is made clear by an example given by plaintiffs' expert, Dr. Mann. Assume on day 1 that ten directed transfers are to be ordered and that only ten postal inspectors are subject to transfer and are 40 years of age and above. Then, assume on day 2 that one directed transfer is to be ordered and that ten postal inspectors under 40 years of age are subject to transfer.


            40+     under 40    directed transfers
     Day 1  10          0               10
     Day 2   0         10                1
            __         __               __
TOTALS      10         10               11

In sum, a total of eleven directed transfers were made from a pool of ten postal inspectors 40 years of age and over and ten postal inspectors under 40 years of age. Using defendant's average data, one-half of the total pool of postal inspectors subject to transfer were under 40 years of age and one-half over 40 years of age. Therefore, one-half of the directed transfers should have been of postal inspectors over 40 and the other half of postal inspectors under 40 years of age. When one looks at the pool of eligible postal inspectors on the two days directed transfers were ordered, however, it is evident that the age-mix of the pool of eligible postal inspectors changed. Because the age-mix of the pool of postal inspectors subject to transfer *22 changed, the use of average data or the binomial distribution is misleading. See PX 57 at 210-11. Using snap shot data, the expected result is not misleading because it reflects what actually occurred. Using such data, ten postal inspectors at least 40 years of age would be transferred on the day 1 and that one postal inspector under 40 years of age would be transferred on day 2, since these were the only postal inspectors subject to transfer when the directed transfers were ordered. Thus, the snap shot data avoids the misleading result obtained by the average data. Accordingly, the Court finds that the use of averages and the binomial distribution upon which defendant's experts base their conclusions is inappropriate in this case because the average age-mix of the eligible postal inspectors changed from day to day. See PX 57.

iii. The Statistics Establishing DISPARATE IMPACT.

Plaintiffs' statistics prove the obvious  that the senior-first rule, by directing the most senior postal inspectors to transfer to the larger and more expensive cities, falls more harshly on postal inspectors 40 years of age and above than on postal inspectors under 40 years of age.
From 1980 through 1985 there was a strong correlation between the age and seniority of level 23 postal inspectors eligible for directed transfers. During this period the correlation coefficients for age and seniority ranged from .3689 to .6657 at a .000 level of significance. See PX 21 & 28. The .000 level of significance means that the odds are one in 1,000 that the correlation between age and seniority would have resulted from chance. Because the odds of this correlation occurring by chance are so small, the correlation must have occurred because age and seniority are related. Thus, the Court finds that the .000 level of significance is statistically significant. See Palmer v. Shultz, 815 F.2d 84, 92 (D.C.Cir. 1987) (.05 level of significance statistically significant); Segar v. Smith, 738 F.2d 1249, 1283 (D.C.Cir.1984), cert. denied, 471 U.S. 1115, 105 S.Ct. 2357, 86 L.Ed.2d 258 (1985) (same).
There is a stronger correlation between age and seniority for all level 23 postal inspectors, ranging from .5714 to .7155 at the .000 level of significance. See PX 22 & 29. There is also a statistically significant correlation between age and seniority for all postal inspectors. The correlation coefficient between age and seniority for all postal inspectors ranges from .5894 to .7236 at the .000 level of significance. See PX 23 & 24. These correlations further suggest that age and seniority are related and, thus, that the senior-first rule has the effect of an older-first rule.
The fact of a definite correlation between age and seniority was and should not have been surprising to defendant, as Dr. Beckett admitted on cross examination that age and seniority were correlated. In sum, whether the Court looks at the eligible level 23 postal inspectors, all level 23 postal inspectors, or all postal inspectors, the Court finds a statistically significant correlation between age and seniority. See PX 21-24, 28-29.
Expectedly, it follows from the correlation between age and seniority that the effect of the senior-first rule falls more harshly on older postal inspectors. Indeed, this is the case. Chief Inspector Clauson conceded that he realized Postal inspectors at least 40 years of age were disproportionately over-represented in the top deciles of the directed transfer list. See also PX 17, 18 & 26. Using a chi-square analysis,[6] the odds are less than one in 1,000 that this over-representation would occur by chance, which means that age and seniority are not independent. See PX 17-20, 26-27. During the first four years of the Policy, there was a 94.7%-100% chance that the postal inspectors at the top of the directed transfer list were 40 years of age and above. See PX 17, 18 & 26. Therefore, at least *23 during the first four years of the Policy there was anywhere from a 94.7%-100% chance that the level 23 postal inspectors at least 40 years of age were subjected to directed transfer first. As more and more level 23 postal inspectors at least 40 years of age volunteered for lateral reassignments or resigned to avoid directed transfers, or were directed to transfer, the number of eligible level 23 postal inspectors at least 40 years of age diminished. Accordingly, it is not surprising that the top deciles of the directed transfer list during the last year of the relevant time period did not contain as many postal inspectors 40 years of age and above as it did from 1980 to 1984. Here, the Court, again notes that the defendant knew of this in the beginning when they adopted the Career Path Policy in question herein. See DX 23 and Clauson Testimony.
The Court also finds that in the top two deciles of postal inspectors eligible for directed transfers from 1980 through 1985 the mean age was at least 40 years. See PX 19 & 20. This also suggests that the level 23 postal inspectors 40 years of age and above were almost always the first to be directed to transfer.
That the senior-first rule had a disproportionately harsh impact on postal inspectors 40 years of age and above is further established by Dr. Mann's results from the Mantel-Haenszel test, which measures the effect of the senior-first rule on the particular days when directed transfers were made. This test should have been utilized by the defendant. Had they done so the result would have been the same as Dr. Mann's result. Dr. Mann proved that there is a statistically significant relationship at the .004 level of significance between age and the probability of receiving a directed transfer. See PX 30. As previously pointed out herein, this test is significant and important because it is not based on averages, but is based on the data collected on or about the time when directed transfers were actually made. Furthermore, the Mantel-Haenszel test shows that it is 1.9 to 2 times more likely that a postal inspector 40 years of age and above will be directed to transfer than a postal inspector under 40 years of age.
It is not surprising then that a statistically significant disproportionate and higher number of postal inspectors 40 years of age and above in fact received directed transfer orders. See PX 25 & 30. Dr. Beckett, the defendant's expert witness, conceded the statistical significance of the disproportionate number of postal inspectors 40 years of age and above that were directed to transfer. Thus, based on all of the above statistics, the Court finds that the senior-first rule had a disproportionately harsh and adverse effect, or disparate impact, on level 23 postal inspectors 40 years of age and above.
In summary, the senior-first rule did what it was designed to do: the rule adversely impacts the plaintiffs by directing the most senior postal inspectors to transfer from the cities, towns, and hamlets across the land to large and expensive cities. An analysis of the multiplicity of statistics in this case establish that seniority was effectively a proxy for age and contrary to law. It caused the senior-first rule to have the effect of an older-first rule, and subjected the older postal inspectors to directed transfers first. Under a theory of disparate impact, it is the effect of the challenged rule that is critical. EEOC v. Borden's, Inc., 724 F.2d at 1394. Thus, plaintiffs have proved the obvious: that the senior-first rule fell more harshly on plaintiffs than on postal inspectors under the age of 40 thereby establishing a violation of the ADEA.

2. No Valid Business Necessity Justifies the Senior-First Rule.

Because plaintiffs' statistics establish that the senior-first rule disparately impacts postal inspectors 40 years of age and older, the burden of persuasion falls upon the defendant to justify its use of the rule by showing a legitimate and nondiscriminatory business necessity for the senior-first rule. Griggs v. Duke Power, 401 U.S. 424, 91 S.Ct. 849, 28 L.Ed.2d 158 (1971); Leftwich, 702 F.2d at 691; Geller, 635 F.2d at 1032. To establish a business *24 necessity, defendant must have had no other choice but to transfer the most senior level 23 postal inspectors to fill the vacancies in the major metropolitan areas. Watkins v. Scott Paper Co., 530 F.2d 1159, 1181 (5th Cir.) ("[B]usiness necessity is limited to those cases where an employer has no other choice" and here the defendant had another choice, i.e., a random method of selection), cert. denied, 429 U.S. 861, 97 S.Ct. 163, 50 L.Ed.2d 139 (1976); Chrapliwy v. Uniroyal, Inc., 458 F.Supp. 252 (N.D. Ind.1977) (business necessity should be narrowly construed and absolutely essential). Furthermore, defendant must show that the senior-first rule bears a "manifest relationship" to the successful performance of the Postal Inspection Service's business needs. Griggs v. Duke Power, 401 U.S. at 424, 432, 91 S.Ct. at 854; Segar, 738 F.2d at 1266-67; Geller, 635 F.2d at 1032.
Chief Inspector Clauson testified that the senior-first rule was justified by the Postal Service's business necessity for (1) more experienced postal inspectors in the major metropolitan areas, (2) a perpetual system for remedying the shortage of experienced postal inspectors in the major metropolitan areas, and (3) a predictable system for directing transfers of experienced postal inspectors to major metropolitan areas. It is clear that defendant has failed to carry its burden of persuading the Court that it had no other choice but to transfer the senior and older postal inspectors to the major metropolitan areas. The entire evidence before the Court and the Policy itself establishes that the defendant did not have a legitimate and non-discriminatory business need for what was done and did in fact have other lawful means of getting sufficient numbers of qualified postal inspectors in the major metropolitan areas without violating the ADEA by utilizing the senior-first rule.
Defendant's real need was for level 21 or higher postal inspectors, regardless of seniority. First, before the most senior level 23 postal inspector was subjected to a directed transfer, a level 23 postal inspector of any seniority could have been allowed to volunteer to fill the vacancy. See PX 16, 35 & 53. Also, if two level 23 postal inspectors volunteered to fill the same vacancy, the postal inspector who bid first could have been given the reassignment even if he or she is less senior than the competing postal inspector. See PX 16, 35 & 53. Thus, defendant's alleged business need could have been satisfied without transferring the most senior and above 40 years of age level 23 in the nation to the high cost of living major metropolitan areas.
Secondly, the most senior level 23 postal inspector would be directed to transfer only if no qualified level 21 postal inspectors of any seniority were to volunteer. See PX 16, 35 & 53. This again indicates the fallacy of the defendant's position as there was only a business necessity to increase the number of level 21 or level 23 postal inspectors of any seniority, rather than the most senior level 23 postal inspectors, in the major metropolitan areas. Indeed, the record shows the fact to be without dispute that the level 21 and less senior level 23 postal inspectors have performed satisfactorily in the major metropolitan areas. An examination of the Career Path Policy itself and the whole record shows unequivocably that the need for "experienced" postal inspectors in the major metropolitan areas could have been met by the reassignment of postal inspectors with far less seniority and rank than the most senior level 23 postal inspector above 40 years of age in the nation.
There is more than ample evidence in the record to show that defendant's alleged need for "experienced" postal inspectors was no more than a need for level 21 and higher postal inspectors. Instead they adopted an illegal Career Path Policy or plan based on age to achieve their end without regard to the law and their own motives were at the least suspect. DX 23. Chief Inspector Clauson testified that level 21 and above postal inspectors of all levels of seniority performed well in the major metropolitan areas. This is not surprising since the complexity of assignments in the major metropolitan areas was not necessarily greater than the complexity of assignments in certain non-major metropolitan areas. Indeed, just prior to implementing the *25 senior-first rule, defendant advertised for level 21 and above postal inspectors to transfer to New York City, the major metropolitan area with the greatest need for experienced postal inspectors. See DX 13A-B & 14 (identifying problem in New York City as lack of experience); DX 15B (notice requesting postal inspectors level 21 and above to relocate to New York City because they possess the necessary experience); PX 34 at 311 (Chief Inspector Clauson's testimony that any level 23, regardless of seniority, qualified to fill the need in major metropolitan areas); PX 33 at 161-62 (Vance Arnold's, Assistant Inspector-in-Charge for New York, testimony that junior level 23 postal inspectors performed fine). Accordingly, the Court finds defendant's need was for qualified level 21 or above postal inspectors regardless of seniority and that the defendant's defense here was and is obviously without merit and pretextual.
Additionally, a task force headed by David Krasula, then Assistant Regional Chief Inspector for Administration of the Northeast Region of the defendant, submitted a report dated September 4, 1979 on the need for experienced postal inspectors in New York City. Mr. Krasula recommended the arbitrary transfer of level 21, 23 and 24 postal inspectors to the New York Division. See DX 14. Based on Mr. Krasula's recommendations, then Chief Inspector Fletcher, in letters dated December 6, 1979 and April 3, 1980, decided that the need for experienced postal inspectors in New York could be filled by nationwide posting of level 23 vacancies and laterally reassigning level 21 postal inspectors. Thus, Assistant Regional Chief Inspector Krasula and Chief Inspector Fletcher both suggested that the need for experienced postal inspectors could be met with level 21 or higher postal inspectors.
As previously indicated, the Court finds that there was another choice to meet the alleged need here and there certainly was no valid business necessity for transferring the most senior level 23 postal inspectors regardless of age and the ADEA to the major metropolitan areas; rather, the choice was to transfer experienced postal inspectors, which would have included level 21 and higher postal inspectors, to the major metropolitan areas rather than the older and most senior level 23 postal inspectors first. The senior-first rule, however, placed the entire burden of this illegal plan for level 21 or above postal inspectors on a narrow class of postal inspectors  the most senior level 23 postal inspectors who were within the protected group because of their age. Accordingly, the Career Path Policy was and is invalid.

3. Even if Defendant Had a Business Necessity to Transfer the Most Senior Level 23 Postal Inspectors, a Non-Discriminatory Alternative Was Available.

"It is clear that business necessity is limited to those cases where an employer has no other choice." Watkins v. Scott Paper Co., 530 F.2d 1159, 1181 (5th Cir.), cert. denied, 429 U.S. 861, 97 S.Ct. 163, 50 L.Ed.2d 139 (1976). Here, a random system was available. See DX 23 and Clauson Testimony. Thus, even if the senior-first rule was justified by a business necessity, plaintiffs would still prevail because another non-discriminatory random system would have met defendant's need for experienced postal inspectors. See Albemarle Paper Co. v. Moody, 422 U.S. 405, 425, 95 S.Ct. 2362, 2375, 45 L.Ed.2d 280 (1975); Geller, 635 F.2d at 1032.
Chief Inspector Clauson testified that he realized the most senior postal inspectors were also the older postal inspectors and that the CPP would adversely affect those older postal inspectors. See also DX 23. Chief Inspector Clauson did consider, however, the use of a random system for making directed transfers and recommended that such a random system be used because it is nondiscriminatory. See DX 23. Chief Inspector Clauson testified on redirect that the only way to correct the adverse effects of the senior-first rule on postal inspectors at least 40 years of age and still accomplish the Postal Service's objectives would be to use a random system. In a July 7, 1980 letter to then Chief *26 Inspector Fletcher, then Assistant Chief Inspector Clauson warned that it is
important that [the transfer system] be logical, nondiscriminatory, and definable. I think there is a good chance, if not certainty, that our actions and decisions will be challenged....
DX 23. Then Assistant Chief Inspector Clauson recommended that eligible postal inspectors be ranked and transferred on a random basis. See DX 23 at 2, ¶ 3. Notwithstanding then Assistant Chief Inspector (now Chief Inspector) Clauson's warnings and recommendations, Chief Inspector Fletcher rejected the random plan.
As already noted, the Court finds that a random system would have satisfied the alleged need for a system for transferring level 21 and above postal inspectors to major metropolitan areas. First, experienced level 21 or higher postal inspectors could have been reassigned to major metropolitan areas either voluntarily or based on random directed transfers. If a sufficient number of postal inspectors did not volunteer, the vacancies could have been filled through random directed transfers. As Chief Inspector Clauson admitted during cross examination, this would have met the understaffing need by increasing the number of experienced postal inspectors in the major metropolitan areas.
Secondly, continual use of the random system would have provided a perpetual system for reassigning experienced postal inspectors to the major metropolitan areas. Postal Inspectors would have had an incentive to volunteer to serve in a major metropolitan area in order to avoid a directed transfer under the random system. This system would have accomplished the same goal as the senior-first rule but without violating the law.
Thirdly, the random system would have been as predictable as the senior-first rule. Because of the senior-first rule's temporary exemptions, a postal inspector's relative place on the directed transfer list changed from day to day. Chief Inspector Clauson and several plaintiffs testified that a postal inspector's relative place on the seniority list changed daily. Notices of rankings on the directed transfer list were discontinued at least once because of inaccuracies due to these daily changes. Because postal inspectors were only notified of their place on the seniority list periodically and the list was always in flux, postal inspectors rarely knew their actual ranking. In addition, postal inspectors never knew for certain when, how many, or to where directed transfers would be made. As a result, many plaintiffs volunteered for lateral reassignments to avoid imminent directed transfers which they heard about through the "grape-vine." In short, the senior-first rule was not all that predictable; a random system would be just as predictable and because it is non-discriminatory it would not impose the entire burden for experienced level 21 or above postal inspectors on the most senior level 23 postal inspectors.

B. The Senior-First Rule Constitutes DISPARATE TREATMENT of Plaintiffs Because Defendant's Use the Rule as a Pretext to Discriminate Against Plaintiffs Because of Their Age.

To prove age discrimination under a theory of disparate treatment, plaintiffs must prove that defendant intentionally discriminated against them because of their age. United States Postal Service v. Aikens, 460 U.S. 711, 715, 103 S.Ct. 1478, 1482, 75 L.Ed.2d 403 (1983); Texas Department of Community Affairs v. Burdine, 450 U.S. 248, 101 S.Ct. 1089, 67 L.Ed.2d 207 (1982). Generally, the order and allocation of proof set forth in McDonnell Douglas Corporation v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973), a Title VII case, applies to cases under the ADEA. Krodel v. Young, 748 F.2d 701, 705 (D.C. Cir.1984), cert. denied, 474 U.S. 817, 106 S.Ct. 62, 88 L.Ed.2d 51 (1985); Coburn v. Pan American World Airways, Inc., 711 F.2d 339, 342-43 (D.D.Cir.), cert. denied, 464 U.S. 994, 104 S.Ct. 488, 78 L.Ed.2d 683 (1983); Cuddy v. Carmen, 694 F.2d 853, 856-57 (D.C.Cir.1982); Johnson v. Lehman, 679 F.2d 918, 922 (D.C.Cir.1982).
Under the tripartite scheme of the McDonnell Douglas case and the cases *27 under the ADEA that have applied that scheme, plaintiffs must first establish a prima facie case by evidence raising an inference of age discrimination. See, e.g., Krodel, 748 F.2d at 705.
Plaintiffs theory of disparate treatment is simple: defendant knew age and seniority were statistically correlated; defendant implemented a seniority-first rule with knowledge that seniority was not a neutral factor with respect to age; therefore, defendant intentionally discriminated against plaintiffs because of their age. In short, plaintiffs claim that seniority was used as a proxy for age. The Court agrees.

1. Plaintiffs' Statistical and Antedotal Evidence Raises an Inference of Discrimination Against Postal Inspectors 40 Years of Age and Over Because of Their Age.

Plaintiffs disparate treatment case, primarily but not exclusively, relies on the statistics showing a statistically significant correlation between eligible level 23 postal inspectors, all level 23 postal inspectors and all postal inspectors. Although plaintiffs may establish a prima facie case raising an inference of discrimination with statistics alone, see Palmer v. Shultz, 815 F.2d 84, 90 (D.C.Cir.1987); Segar, 738 F.2d at 1278-79, there is additional evidence which is probative on this issue. See Palmer, 815 F.2d at 90. Chief Inspector Clauson testified that he knew age and seniority were correlated and that the senior-first rule would adversely affect the older postal inspectors. Despite Chief Inspector Clauson's premonition in his letter to then Chief Inspector Fletcher that the senior-first rule would be challenged and a non-discriminatory system should be used, see DX 23, defendant implemented the Rule without regard to its effect on postal inspectors 40 years of age and over and its legality under the ADEA. The Court finds that defendant's disregard of the adverse effect of the Rule on postal inspectors 40 years of age and over and the correlation between age and seniority raise far more than an inference of age discrimination. Thus, plaintiffs have established a prima facie case of discrimination under a theory of disparate treatment.

2. Defendant Has Not Sustained Its Burden of Producing Evidence of a Legitimate, Non-Discriminatory Business Reason for the Senior-First Rule.

Since plaintiffs have established a prima facie case of discrimination, defendant must proffer evidence of a legitimate, non-discriminatory reason for its actions. See, e.g., Krodel, 748 F.2d at 705. Defendant asserts that the senior-first rule is a perpetual and predictable system for transferring experienced postal inspectors to major metropolitan areas. This is not, however, a legitimate, nondiscriminatory reason for using the senior-first rule. Burdine, 450 U.S. at 253, 101 S.Ct. at 1093; Krodel, 748 F.2d at 705. As discussed in the disparate impact section above, there was no valid need for defendant to transfer the most senior level 23 postal inspectors, particularly under a senior-first rule which discriminates on the basis of age. Therefore, the Court finds that defendant has not sustained its burden of production.

3. Plaintiffs' Have Proven by a Preponderence of the Evidence That Defendant's Reason for the Senior-First Rule Was But a Pretext for Its Discriminatory Animus.

Assuming defendant met its burden of production above, plaintiffs must show by a preponderance of the evidence that defendant's proffered reason was a pretext to mask its illicit motive to discriminate against plaintiffs because of their age. Id. Plaintiffs must prove that age made a difference in defendant's decision to transfer them in the sense that, but for defendant's discriminatory motive, plaintiffs would not have been transferred. See, e.g., Krodel, 748 F.2d at 706.
Upon consideration of all the evidence, the Court finds that plaintiffs have proved by a preponderance of the evidence that the senior-first rule was a pretext for age discrimination in this case and the defendant knew this. See DX 23. Defendant knew that seniority and age were correlated and that the senior-first rule would have the same effect as an older-first rule. Moreover, as repeatedly stated herein, defendant's *28 need was not for the most senior level 23 postal inspectors, but for level 21 or higher postal inspectors. Nevertheless, defendant directed transfers pursuant to a rule that transferred the most senior level 23 postal inspectors first. Defendant used the senior-first rule despite the availability of a non-discriminatory random system. Thus, the Court concludes, based on all the evidence in the record, including that evidence discussed above, that the senior-first rule was a pretext to mask its discriminatory animus and motive. Accordingly, plaintiffs have proved a case of disparate treatment.

4. Defendant Knew the Senior-First Rule Violated the ADEA and, Therefore, Defendant's Conduct Was Willful.

For the reasons set forth above, particularly the testimony of Chief Inspector Clauson and DX 23, the Court finds that defendant willfully violated the ADEA when it forced senior postal inspectors to transfer to cities such as New York City. Defendant knew that a senior-first rule would require the older and most senior postal inspectors to transfer against their will. Indeed, that the senior-first rule transferred the older postal inspectors first was no surprise to defendant; this was precisely what defendant intended. As Chief Inspector Clauson admitted, the senior-first rule was chosen over a junior-first rule because the Postal Inspection Service wanted to force the senior postal inspectors to fill the vacancies that were not voluntarily filled  the least desireable vacancies. Moreover, defendant was well aware that age and seniority were correlated, as plaintiff proved with a multiplicity of statistics. Again, that defendant knew of the correlation between age and seniority was admitted by Chief Inspector Clauson. Finally, DX 23 not only warned of the consequences of implementing a discriminatory senior-first rule, but also recommended the use of a non-discriminatory random system. Upon consideration of all the evidence, including that discussed above, the Court finds that defendant knew the senior-first rule violated the ADEA, but implemented the Rule anyway, thus constituting a willful violation of the ADEA. See, e.g., Trans World Airlines v. Thurston, 469 U.S. 111, 105 S.Ct. 613, 83 L.Ed.2d 523 (1985).

VI. CONCLUSION
Upon thorough consideration of the record, including the testimony, the exhibits, and based upon the Court's judgment as to the credibility of the witnesses herein, the Court certifies this case as a Rule 23(b)(2) class action, grants defendant's motion to dismiss plaintiffs Brady and Rittiner as class representatives, but denies defendant's motion to dismiss Brady and Rittiner as class members, and finds that the plaintiffs did not waive their rights under the ADEA when they were unlawfully directed to transfer. More importantly, the Court finds that plaintiffs have proved that the senior-first rule violates the ADEA under a theory of both disparate treatment or disparate impact. Accordingly, the Court will issue an order of even date herewith consistent with this Opinion.

ORDER
For the reasons set forth in the Opinion of even date herewith, it is, by the Court, this 13th day of August, 1987,
ORDERED that this case is certified as a Federal Rule of Civil Procedure 23(b)(2) class action to include
All postal inspectors of the United States Postal Service between December 1, 1980 and September 1, 1985 who were, are, or have been affected by the senior-first rule of the Career Path Policy.
and, it is
FURTHER ORDERED that defendant's motion to dismiss plaintiffs Brady and Rittiner as class representatives is granted; and, it is
FURTHER ORDERED that defendant's motion to dismiss plaintiffs Brady and Rittiner as class members is denied; and, it is
FURTHER ORDERED that all of the class representatives and class members Brady and Rittiner have standing to challenge the senior-first rule; and, it is
FURTHER ORDERED that the plaintiffs did not waive their rights to challenge the senior-first rule as a violation of the ADEA; and, it is
*29 FURTHER ORDERED that the senior-first rule of the Career Path Policy has a disparate impact on and causes disparate treatment of postal inspectors 40 years of age and above; and, it is
FURTHER ORDERED that the defendant's conduct herein was willful within the meaning of the Age Discrimination in Employment Act for the reasons set forth in the Court's Opinion of this date; and, it is
FURTHER ORDERED that the senior-first rule of the Career Path Policy is hereby declared to be unlawful and in violation of the Act insofar as it pertains to level 23 postal inspectors; and, it is
FURTHER ORDERED that defendant is hereby enjoined from ordering transfers pursuant to the senior-first rule of the Career Path Policy; and, it is
FURTHER ORDERED that the parties confer in person and file with the Court within ten days of receipt of this Order and Opinion a joint stipulation setting forth suggestions as to the remedies phase of this case, keeping in mind that expeditious resolution of the remedies phase by reference to a special master or other means may be appropriate.
NOTES
[1]  This Opinion shall constitute the Court's findings of fact and conclusions of law pursuant to Federal Rule of Civil Procedure 52(a).
[2]  Fourteen cities have been designated by the United States Postal Inspection Service as major metropolitan areas: New York, Los Angeles, Chicago, Philadelphia, Detroit, Houston, Boston, San Francisco, Oakland, Washington, D.C., St. Louis, Cleveland, Miami and Newark. See Plaintiffs' Exhibit ("PX") 16.
[3]  This promotion schedule commenced in late 1983. Prior to 1983, postal inspectors were promoted to level 19 after one year of satisfactory service at level 17, were then promoted to level 21 after one and one-half years of satisfactory service at level 19, and were promoted to level 23 on a competitive basis regardless of the amount of time served at level 21.
[4]  The binomial distribution predicts the probability of transferring a postal inspector 40 years of age and older when chosen from a pool consisting of eligible postal inspectors over 40 years of age and under 40 years of age. An important caveat, however, is that the binomial distribution is valid only under three conditions: 1) each directed transfer is dichotomous, in other words, there are only two possible outcomes  that a postal inspector will be directed to transfer or will not be directed to transfer; 2) each time a directed transfer is ordered the probability of transferring a postal inspector 40 years of age and older remains constant and is in fact equal to the probability of transferring a postal inspector 40 years of age and older; and 3) the each directed transfer is independent. See Cangelosi, Taylor and Rice, Basic Statistics, A Real World Approach at 30 (West 1979). Because the age-mix of the pool of eligible postal inspectors changes daily, the probability of transferring a postal inspector 40 years of age and older does not remain constant as required by condition 2 above.
[5]  An average or arithmatical mean is the sum of a set of observations divided by the number of observations. Id. at 25-30.
[6]  The chi-square analysis is useful in this case because it makes "no assumptions about the value of a parameter." In other words, it is useful when, as in this case, the population distribution, or the age-mix of postal inspectors here, is unknown. See Cangelosi, Taylor and Rice, Basic Statistics, A Real World Approach at 248 (West 1979).
