Opinion for the Court filed by Circuit Judge WILLIAMS.

WILLIAMS, Circuit Judge:

This case appears before us on appeal for the third time. A sex discrimination class action against the United States Information Agency (“USIA”), it has been working its way up and down the system for nearly 20 years. The end may be at hand — or at least further progress into the remedial phase may be. We find most of defendant’s arguments — which concern both certification and liability — to be either waived or barred by law of the case. We affirm the judgment except as it concerns the individual claim of plaintiff Carolee Brady (Hartman) and the decision setting aside 39 foreign service officer slots to be filled by class members.

*1235 The facts and procedural posture of this case are described at length in our second pass at it, Hartman v. Duffey, 19 F.3d 1459, 1461-63 (D.C.Cir.1994), so we will give only a brief summary here. In November 1977 Carolee Brady Hartman 1 filed a sex discrimination class action against the USIA, and in April 1978 the district court conditionally certified a class of women under F.R. Civ. Pro. 23(b)(2). After the parties agreed to bifurcate the trial into a liability and a remedy stage, the district court held a bench trial on class liability and found that plaintiffs had failed to establish a prima facie case of sex discrimination. De Medina v. Reinhardt, 21 Fair Empl. Prac. Cas. (BNA) 75, 1979 WL 39 (D.D.C.1979). On the first appeal, we reversed the dismissal of the hiring discrimination claim because we found error in the court’s treatment of the statistical evidence. De Medina v. Reinhardt, 686 F.2d 997, 1002 (D.C.Cir.1982). On remand, the district court found that the USIA had discriminated against women in hiring for six occupational categories. Hartman v. Wick, 600 F.Supp. 361 (D.D.C.1984). In 1988 the district court laid out the framework for relief, Hartman v. Wick, 678 F.Supp. 312 (D.D.C.1988), ruling that unless the parties agreed otherwise, class members who applied for civil service positions were to be given “Teamsters” hearings to determine relief on an individual basis. See International Bhd. of Teamsters v. United States, 431 U.S. 324, 372, 97 S.Ct. 1843, 1873, 52 L.Ed.2d 396 (1977). 2 For applicants for foreign service jobs, the district court in 1992 set aside 39 slots to be filled by class members over the next three years. Hartman v. Gelb, No. 77-2019 (D.D.C. July 9, 1992) (“July 1992 order”). The USIA appealed.

On the second appeal, we addressed only the question of class certification, saying that the record did not adequately demonstrate that a class existed. 19 F.3d at 1472. We remanded, holding that “plaintiffs must make a significant showing to permit the court to infer that members of the class suffered from a common policy of discrimination that pervaded all of the employer’s challenged employment decisions.” 19 F.3d at 1472 (analyzing General Tel. Co. v. Falcon, 457 U.S. 147, 159, 102 S.Ct. 2364, 2371, 72 L.Ed.2d 740 (1982)).

After our remand, twenty class members representing the six job categories petitioned for intervention as named plaintiffs, and the district court approved intervention as of right under F.R. Civ. Pro. 24. Hartman v. Duffey, 158 F.R.D. 525, 535-36 (D.D.C.1994). He further found that the class was properly certified both in 1978 and now, holding that plaintiffs had identified four discriminatory practices that demonstrated a common policy of discrimination sufficient to support the initial class certification. Id. at 538-39. (We return to these practices later.)

The USIA now appeals again, asserting a variety of errors. Primarily because of law of the case and waiver, we reject all of defendant’s arguments except those specifically concerning Hartman herself and the 39 foreign service slots.

I. Vicarious Exhaustion of Administrative Remedies

The USIA argued to the district court on the latest go-around that class members should not be permitted to intervene as additional named plaintiffs because they had failed to exhaust their administrative remedies. 158 F.R.D. at 535. The district court applied this court’s doctrine of vicarious exhaustion-that exhaustion of administrative remedies by one member of the class satis- fies the requirement for all others with sufficiently similar grievances, see Foster v. Gueory, 655 F.2d 1319, 1322-23 (D.C.Cir.1981)-and therefore allowed the interven- tion. On this appeal, the USIA disputes the to the defendant to *1236 district court's application of the vicarious exhaustion doctrine, claiming among other things that the few administrative complaints actually filed were not precise enough to fulfill the purposes of the doctrine, such as putting the agency on notice and allowing for administrative resolution of the claims.

We do not reach the merits of defendant's arguments on this issue because of the defendant's failure to pursue it in its prior appeal. "jjW]here an argument could have been raised on an initial appeal, it is inappropriate to consider that argument on a second appeal following remand." Northwestern Indiana Tel. Co. v. FCC, 872 F.2d 465, 470 (D.C.Cir.1989). The rule serves judicial economy by forcing parties to raise issues whose resolution might spare the court and parties later rounds of remands and appeals. Crocker v. Piedmont Aviation, Inc., 49 F.3d 735, 740 (D.C.Cir.1995).

The USIA had ample opportunity to raise the exhaustion issue on its previous appeal when it challenged class certification. Its theory here depends simply on the absence of individual exhaustion and on the vagueness of the administrative complaints of those who did exhaust. As the vast majority of the members of the class have not exhausted their administrative remedies (and in fact the intervenors are and have always been members of the class), the filing of petitions for intervention as named plaintiffs did nothing to enhance defendant's abifity to raise the issue of exhaustion by plaintiffs who in fact failed to exhaust their remedies personally. By arguing the exhaustion point at the appropriate (much earlier) juncture, the USIA could perhaps have undone certification at one stroke. Instead, the agency waited to raise this issue until this late date, almost two decades into litigation and after our second opinion in this case focusing almost exclusively on class certification. The omission is all the more striking because the issue had come up in the course of the litigation before with respect to one named plaintiff. See De Medina, 686 F.2d at 1012-13 (finding that the vicarious exhaustion doctrine of Foster applied to named plaintiff Kobylinski, whose claims were "virtually identical" to those of named plaintiff Martinez, who had exhausted). We therefore find no error in the district court's order permitting the intervention of additional named plaintiffs.

We note that plaintiffs did not raise this waiver problem. We have in some instances found such silence to be a waiver of a waiver, see, e.g., Belton v. WMATA. 20 F.3d 1197, 1202 (D.C.Cir.1994); Fox v. District of Columbia, 83 F.3d 1491, 1496 (D.C.Cir.1996), but we do not do so here. 3 We think it would be in only the most extraordinary case that a second-time appellant could escape the consequences of its earlier omission at the end of nearly twenty years of litigation.

II. Hartman's Individual Claims

We do find one aspect of defendant's arguments about lack of vicarious exhaustion to be not waived-and persuasive: that Hartman herself is out of the case because the district court had earlier found that she was not qualified for the job she sought. The only personnel action that Hartman claimed had injured her was rejection of her application for a job on Horizons Magazine, a USIA publication. In its 1979 opinion rejecting class certification, the district court noted that "{b]oth Ms. Dorothy Crook, then Senior Editor of Economic Impac4 another Agency publication, and Mr. Robert Koren-gold, then Editor of Horizons Magazine, testified that Ms. Hartman could not have been seriously considered for the position as she did not possess sufficient professional journalism experience." 21 Fair Empl. Prac. Cas. at 80. The court credited this testimony, writing: "The Court conclusively accepts the testimony of Ms. Crook and Mr. Koren-gold on this matter." Id. (emphasis added).

That conclusion lay fallow in the record until the most recent remand, when the trial *1237 court's apparent change of mind surfaced accidentally. The goveriiment pointed out the prior conclusive finding against Ms. Hartman in connection with the analysis of typicality (for certification purposes), 158 F.R.D. at 545, only to be told by the district court: "[Tihis Court neither heard nor made a final determination on the merits of Ms. Hartman's individual claim. Ms. Hartman's claim, like those of every other class member who applied for a civil service position, is subject to an individual Teamsters hearing before the Special Master." Id. at 546.

We do not understand in what sense the district court can mean that its prior "conclusive[ ]" finding was non-final. Although not the subject of a separate judgment under Rule 54 of the Federal Rules of Civil Procedure, it was a "conclusive" ruling that was embraced by the final judgment that was the subject of the first appeal, decided in 1982. (And our decision on the first appeal did not overturn that specific finding.) In an apparent effort to suggest an exception to the application of law of the case to the issue, the district court observed that plaintiffs cited the affidavit of a USIA Personnel Management Specialist saying that he thought Hartman was qualified for a GS-11 or -12 position in "editorial-type" work. Id. at 545-46 n. 16. (The Horizons Magazine job was the equivalent of GS-11 or -12.) But this was among the evidence the trial court considered in arriving at its earlier decision, and so does not fit under the exception for new evidence. In any event the personnel specialist was not addressing specific qualifications for the Horizons Magazine job. Although piaintiffs suggest no other reason why the finding against Hartman is not in fact "conclusive" under law of the case, in truth the defendant raised the issue only rather obliquely; we remand the case in light of the possibifity that there is some overlooked exception to law of the case that might permit revival of her individual claim.

III. The Propriety of Class Certification

Our most recent (1994) opinion dealt at length with the question of class certification in this case, analyzing in considerable detail the Supreme Court's exposition in General Tel. Co. v. Falcon,, 457 U.S. 147, 102 S.Ct. 2364, 72 L.Ed.2d 740 (1982), of the commonality requirement in discrimination class actions. See 19 F.3d at 1469-70. We observed that the "principal problem" with certification in this ease was that the class "encompasses both civil service and foreign service applicants to the USIA, despite the fact that the two categories are hired under different personnel systems." Id. at 1471. Although the latest district court opinion understandably spent considerable time showing that the claimed discriminatory practices cut across both civil and foreign service categories, see, e.g., 158 F.R.D. at 536-37, 541, 546, the USIA has not, so far as class certification is concerned, addressed the civil service/foreign service difficulty at all on this appeal. So that issue is out of the case.

There remains the general question whether plaintiffs showed sufficient commonality and typicality among the members of the plaintiff class. Under our prior instructions, the district court-as we noted above-identified four "practices" evidencing a common policy of discrimination that largely cut across job categories. 158 F.R.D. at 539. The defendant argues that these supposed "practices" amount simply to anecdotal evidence of subjective discrimination. We need not resolve that claim, however, for even if we resolved it in the defendant's favor we would not find an abuse of discretion in the class certification. Wagner v. Taylor, 836 F.2d 578, 588 (D.C.Cir.1987) (reviewing for abuse of discretion). In our most recent pass at this case, we hesitated to suggest that the certffication finding might be based on statistical evidence alone. Hartman, 19 F.3d at 1474. We expressed concern that some of the statistical evidence might have been "premised on the (improper) class certification," id., a concern that appears to have been significantly driven by the plaintiffs' blurring of lines between the civil service and the foreign service. But with that issue completely out of the case, and with the defendant making no argument as to why the statistical evidence would not have been admissible in trials of individual cases brought on behalf of any particular class member, the case no longer appears to present any reason *1238 for that concern. Accordingly, we find no properly preserved error in the class certification.

IV. The 1984 Finding of Liability

After the first remand from this court in 1982, neither party sought to introduce new evidence but agreed to submit on the existing record. 600 F.Supp. at 362-63. On the last appeal, referring to the defendant's later effort to introduce new statistics differentiating between the civil and foreign services, we observed that the district court's decision whether to consider new evidence after the close of the liability portion of a bifurcated trial was reviewed only for abuse of discretion. 19 F.3d at 1473 (citing Segar v. Smith, 738 F.2d 1249, 1285 (D.C.Cir.1984)). The USIA has again sought to offer new statistical analyses of data in the record, which the district court did not consider. We find no abuse of discretion.

First, the USIA now argues for two-tailed statistical analysis, as opposed to the one-tailed analysis actually performed for trial by plaintiffs' expert. The differences between two-tailed and one-tailed analysis are described in Palmer v. Shultz, 815 F.2d 84, 94 (D.C.Cir.1987), which ultimately favors two-tailed analysis for Title VII purposes, id. at 95. The key distinction is that one-tailed analysis tests whether a group is disfavored in hiring decisions while two-tailed analysis tests whether the group is preferred or disfavored. In two-tailed analysis, a larger difference (measured in standard deviations) between the actual incidence of (say) hiring of a class and the "expected value" is necessary before a social scientist would reject the inference that the difference was random. Id. at 92-96. On appeal, defendant offers new calculations of standard deviations that it claims reveal no statistically significant disparities in two job categories, using two-tailed analysis for the first time. But because defendant offered no calculations of standard deviations at all at trial, and indeed never objected to plaintiffs' expert's use of one-tailed analysis, we reject the claim.

For similar reasons, we reject defendant's claim that the district court should have considered yearly hiring statistics rather than the static "snapshot" statistics plaintiffs' expert provided (which might incorporate pre-Civil Rights Act discrimination). At trial, the defendant's expert presented hiring statistics in raw form only, with no effort to compute standard deviations or otherwise offer statistical analysis. In its reply brief the USIA essentially argues that the district court should have calculated the standard deviations itself, an argument plainly inconsistent `with the conventional requirement that each party present the evidence and arguments on its side of a case.

On the question of whether civil and foreign service hires should be separated for statistical purposes, the USIA, in contrast to its silence on the point as regards class certification, argues on the liability issue in favor of such separation. But this is not only not the position it presented at trial, but is the opposite of it. At trial defendant's expert insisted that the Foreign Information Specialist Category (which was mostly made up of foreign service officers) could not be separated from the other job categories (mostly made up of civil service members) that he aggregated and compared with the census category "Editors and Reporters."

Finally, the USIA challenges the district court's 1984 "cross-mapping" for the job category of foreign language broadcaster. "Cross-mapping" refers to the process by which the plaintiffs compared the male-female composition of the workforce in various USIA categories with the male-female composition nationwide in various private-sector job categories defined by the U.S. Census Bureau. The district court found plaintiffs' expert's choice of the Editors and Reporters census category to be "well-reasoned," 600 F.Supp. at 374, rejecting the defendant's preference for the Radio Announcer category. The USIA now argues that broadcasting and announcing experience was an "essential minimum qualification" for the job. But the position description in the record suggests that the requirement was simply one of "a voice suitable for international broadcasting," and other evidence indicates that men were hired for the position despite lack of broadcasting experience. Under the "clearly erro *1239 neous" standard, see De Medina, 686 F.2d at 1007, we find no reversible error in the district court's factual finding.

The USIA also claims that the district court should not have reaffirmed its liability finding given the new alleged discriminatory practices and evidence from intervenors. But the agency confuses the issues of certification and liabifity. The in-tervenors here, who were already members of the class, sought to become named plaintiffs and introduce evidence solely for purposes of certification; the evidence does not go to liability. The defendant having failed to show any properly preserved error in the analysis by which the district court reached its prior finding of liabifity, the new evidence is unnecessary to plaintiffs' success on that issue. Moreover, as the district court pointed out, the intervention would not adversely affect the anticipated remedial proceedings, as the interve-nors who were civil service applicants would simply participate in Teamsters hearings just as they would have as class members, and those who were foreign service applicants would simply join others already seeking the 39 slots the court had set aside. 158 F.R.D. at 532 n. 3. We therefore affirm the district court's refusal to reopen its finding of liability.

V. The 39 Foreign Service Slots

Finally, the USIA objects that in the remedial phase of the case the district court set aside too many foreign service slots to be filled by class members because it included hiring shortfalls for 1985. (Although all 39 slots were to be filled as of December 1995, we do not believe the claim is moot, because, as the parties seem to agree, there is a reasonably high probability of continuing disputes over seniority, the effects of reductions in force, and similar issues.) The problem is that the district court had earlier ruled that "the Defendant's liability ceased as a matter of law" on November 16, 1984, see July 1992 order at 6 n.4, which seems to preclude reliance on inferred hiring shortfalls for 1985 as a basis for creation of remedial slots.

The district court arrived at the figure of 39 by relying on the model of one Dr. Siskin, called by plaintiffs, that was presented at a 1987 hearing on remedies. Id. at 10-12. Siskin calculated shortfalls in female hiring of foreign service officers for the years 1979-85, see Joint Appendix 497, which the district court characterized as data for 1978-84, July 1992 order at 12. This apparent error may have beefed up the slot calculation by about ten positions, as the USIA claims, but of course there is also the problem that Siskin's data did not cover 1978 (the first year for which remedy was to be had, id. at 2). We accordingly remand the case to the district court to sort out this conundrum.

* * *

We therefore affirm the district court in most respects, remanding only for consideration of why named plaintiff Hartman's individual claims should not be dismissed and for re-examination of the number of foreign service slots set aside.

So ordered.

Notes

. Ms. Hartman later changed her name to Brady, but in order to reduce confusion we wUl follow the parties in continuing to use the name Hartman.

. At a Teamsters hearing each plaintiff must show by a preponderance of the evidence that she applied for a job during the relevant time period and was rejected. The burden then shifts show that there was a legitimate reason for not hiring the applicant. If defendant meets that burden, the plaintiff can offer evidence indicating that the proffered reason is simply a pretext for discrimination. See Hartman v. Wick, 678 F.Supp. at 335; Hartman v. Duffey, 19 F.3d at 1462 n. 2. at 1462 n. 2.

. The Supreme Court has held that the require-merit that a Title VII plaintiff file a timely complaint with the EEOC before gaining access to the courts is not jurisdictional, meaning that it can be waived and-most importantly for purposes of rejecting waiver of waiver-that we need not raise the exhaustion issue on our own initiative. Zipes v. Trans World Airlines, 455 U.s. 385, 392-98, 102 S.Ct. 1127, 1131-35, 71 L.Ed.2d 234 (1982).