
    Nicholas Reyes LOPEZ, et al., Plaintiffs, Jesus Botello and Francisco Gonzales, Plaintiffs-Appellants, v. LABORERS INTERNATIONAL UNION LOCAL # 18 and Laborers International Union of North America, Defendants-Appellees.
    No. 92-2315.
    United States Court of Appeals, Fifth Circuit.
    April 14, 1993.
    
      Ruben Rendon, Gloria Briseno, Houston, TX, for plaintiffs-appellants.
    James R. Watson, Watson, Flynn & Ben-sik, Galveston, TX, for Laborers Intern. Union Local # 18.
    Michael Barrett, Theodore T. Green, Washington, DC, for Laborers Intern. Union of North America.
    Before REAVLEY, KING, and WIENER, Circuit Judges.
   PER CURIAM:

In this employment discrimination lawsuit, Plaintiffs-Appellants, Nicholas Lopez, as attempted class representative, Jesus Botello, and Francisco Gonzalez (collectively Lopez et al.), assert that the district court erred in granting summary judgment in favor of Defendants-Appellees, Laborers International Union Local # 18 and Laborers International Union of North Amer-ica (collectively the Union). Lopez et al.’s claims of discrimination, resting on both disparate impact and disparate treatment theories, were constructed by use of statistical evidence that the district court found inadequate to prove a prima facie case. Our plenary review leads us to the same conclusion reached by the district court in granting summary judgment, so we affirm.

I

FACTS AND PROCEDURAL HISTORY

The local union entered into a collective bargaining agreement (CBA) with employers of laborers on construction projects in the Houston area. The agreement specified terms and conditions of employment that included a referral system for out-of-work laborers, which system involved the use of a so-called “roll call” list. Under the CBA’s referral rules, each unemployed laborer was entitled to sign the list and wait for work (for which the laborer had the requisite skills) to become available. The roll call system operated on a first-come-first-served basis, i.e., the laborer whose name had made it to the top of the list would get the next call. If for any reason that worker did not take the job, it would be offered to the next laborer in line. Once a laborer was referred to a job, his name would be removed from the list. Then, after completion of the work thus obtained, the laborer would again be eligible to sign the list and wait for work. If he did so, he had to start over at the bottom of the list and wait until his name again made it to the top before he would become eligible for another referral.

There were two exceptions to the first-come-first-served rule of the referral system. Under one exception laborers were free to seek work on their own, in which case neither they nor the employer would use the referral system. The other and more important exception allowed employers to call the union hiring hall and ask for individual workers by name. A laborer thus expressly requested would get the job regardless of whether at that time he was signed onto the roll call list or, if he was, regardless of his relative position on that list.

The genesis of this lawsuit was an incident involving one of the employers who had contracted with the Union to use the roll call system — Ric Gunite Refractories, Inc. (Gunite). Lopez et al. allege that after Gunite called the Union and had several Hispanic workers (Lopez, Botello, and Gonzalez) referred to its work site, Gunite refused to hire them, thus failing to comply with the referral system. After learning of Gunite’s refusal to hire the Hispanics, representatives of the Union referred Lopez et al. to the EEOC and even drove those laborers to the EEOC office.

Lopez et al. discussed the incident and other problems with the EEOC representatives, then filed employment discrimination claims with the EEOC against both Gunite and the Union — Gunite for the above described incident and the Union for maintaining an allegedly discriminatory referral system. The Hispanic laborers reasoned that allowing employers to request individual laborers by name had a discriminatory effect on their group.

The EEOC investigated the claims and found reasonable cause to believe that the local union had discriminated on the basis of national origin. The EEOC found three specific grounds: 1) maintaining a discriminatory referral system that allowed employers to request workers by name; 2) failing to oppose employers’ requests that adversely affected Hispanic referrals; and 3) failing to oppose Gunite’s actions after becoming aware of allegations of unlawful discrimination. Conciliation efforts were unsuccessful, and the EEOC eventually issued a right-to-sue letter. Lopez et al. timely sued Gunite, the local union and the international union.

As discovery progressed, Lopez et al. dropped Gunite from the lawsuit. In response to the Union’s motion, the district court adopted the magistrate’s memorandum and recommendation, granting summary judgment in favor of the Union. The district court found that Lopez et al. had failed to make out a prima facie case of discrimination under either a disparate impact or disparate treatment theory.

In its discussion of Lopez et al.’s disparate impact claim, the district court addressed two of the critical elements of a discrimination suit that were discussed in Wards Cove. The court found that Lopez et al.’s own statistics failed to demonstrate a racial imbalance produced by the referral system. In fact, noted the district court, Lopez et al.’s statistics showed a higher percentage of Hispanics receiving referrals than the percentage of Hispanics in the eligible labor pool. The court also found that Lopez et al. failed to isolate and identify specific practices responsible for the perceived statistical disparities. The court therefore granted summary judgment in favor of the Union concerning the disparate impact claims as Lopez et al. failed to. prove a prima facie case.

The district court also granted summary judgment in favor of the Union on Lopez et al.’s disparate treatment claims. The court found that nothing more than bare allegations supported those claims, and that Lopez et al. failed to establish any discriminatory pattern or practice. Lopez et al. timely appealed.

II

ANALYSIS

A. Standard of Review

It is well established that, on appeal from a district court’s grant of summary judgment, we review the record “under the same standards which guided the district court.” The standards we apply are set out in the Supreme Court trilogy of Anderson v. Liberty Lobby, Inc., Celotex Corp. v. Catrett, and Matsushita Electric Industrial Co. v. Zenith Radio Corp. Summary judgment is proper when no issue of material fact exists and the moving party is entitled to judgment as a matter of law. In determining whether summary judgment was proper, all fact questions are viewed in the light most favorable to the non-movant. Questions of law are reviewed, as they are in other contexts, de novo.

B. Lopez et al.’s Claims

As was observed in the Union’s brief to this court and again at oral argument, the summary judgment evidence filed by Lopez et al. suffered from several evidentiary problems. For the purpose of simplifying this appeal, however, we shall assume arguendo that all of Lopez et al.’s summary judgment evidence was validly presented to the court (i.e., properly authenticated and timely filed), and that such evidence at least facially implicates genuine issues of material fact.

In attempting to prove a prima facie case of Union discrimination against Hispanics, Lopez et al. submitted statistical evidence of a disparity between the number of Hispanics hired in the Roll Call system and the number of Hispanics hired by specific requests from employers. To put it bluntly, that comparison is apropos of nothing. The district court held that the comparison made by Lopez et al. was inadequate as a matter of law under Wards Cove. Specifically, that court stated:

Plaintiffs have gone to great lengths in their attempts to show statistically that the Union practice of allowing employers to request workers by name has a negative impact upon the number of Hispanics hired. In fact, their own statistics demonstrate the contrary, that the practice of allowing employers to request workers by name results in a higher percentage of Hispanics receiving work referrals from the union. Plaintiffs’ attempts to find a statistically significant difference between the number of Hispanics referred from the roll call list and those requested by employers are unpersuasive and reflect an imperfect understanding of the relevant points of comparison.

On appeal Lopez et al. argue to us that it was the district court and not they who misinterpreted the statistics that were offered as proof of discrimination. They argue that their expert “concluded that an analysis of the data from the period 1984— 1986 indicates that the difference in percentage of Hispanics introduced from out-, side the roll call lists and those from the roll call lists is statistically significant. No analysis is made of the roll-call list and the number of Hispanics [sic] workers requested by employers.”

Our independent review of the summary judgment evidence presented by Lopez et al. convinces us that the district court was correct in finding that Lopez et al. had an “imperfect understanding of the relevant points of comparison.” Essentially, Lopez et al.’s statistics fall into one of two sets, neither of which are competent to prove discrimination. The first set purports to be a comparison between 1) the number of Hispanics on the roll call lists and 2) the number of referrals that went to Hispanics from outside of that list. According to Lopez et al.’s expert, Hispanics make up 31% of the workers introduced from the roll call lists. That percentage is compared with the percentage of Hispanics who received work (were “introduced to employers”) “from outside the Row [sic] Call lists”—23%. Lopez et al. conclude that the difference between those two percentages alone—“3.01 Standard Deviations”—is “statistically significant” and demonstrates racial discrimination.

The second set of statistics relied on by Lopez et al. purports to be a comparison between 1) the percentages of Hispanic workers among all workers specifically requested by employers and 2) the percentages of Hispanic workers among all who were introduced from the “TWI records,” i.e., from the roll call list. The expert’s report indicates that 31% of the specific requests by name were for Hispanic workers. That percentage is compared with the total number of Hispanics introduced to employers during the requisite period from the TWI records — 26%. Again, Lopez et al. declare that this disparity alone — “3.26 Standard Deviations ” — is “statistically significant” and demonstrates racial discrimination.

The essence of Lopez et al.’s assertion of error is that both sets of statistics independently demonstrate discrimination — that both sets contain a disparity greater than three standard deviations between the number of Hispanics in the labor pool and the number of Hispanics referred either from the roll call or via specific requests. Lopez et al. argue that as the percentages hired through the two different systems are more than three standard deviations from the percentage that should comprise that group, a prima facie case has been made out.

For more than a decade, we have recognized that a prima facie case of discrimination can be made out with statistics alone when “a ‘gross’ disparity in treatment of workers based on race is shown.” We have further recognized that “[a] deviation greater than three standard deviations is prima facie proof that the selection system is not random.” Seizing on those two abstract generalities of employment discrimination law, Lopez et al. argue that, as they have presented statistics over the three standard deviations threshold, the district court should have found that they made out a prima facie case.

Even assuming the applicability of our statement in Williams as to a prima facie case being provable by demonstrating a disparity of three standard deviations, Lopez et al.’s statistics are fatally flawed. True, they have concocted numbers to create the requisite standard deviations, but they have done so on the basis of completely inappropriate data. The starting point or base of Lopez et al.’s (or any) standard deviation model must be the probability of a member of the suspect class’s being employed in a particular position — i.e., the percentage of the minority group in the relevant labor pool. In Williams, for instance, African Americans constituted 75% of the workers in the available pool. For purposes of the statistical analysis in Williams, therefore, African Americans had a 75% chance of receiving the job assignment in question.

In both of Lopez et al.’s statistical models, the probability of Hispanics that is represented as the base figure (the probability of a Hispanic being referred) is 31%. Unfortunately for Lopez, et al., however, the numbers used to create this base statistic in both sets of figures are simply irrelevant to any effort to demonstrate employment discrimination.

As for the percentages of Hispanics on the roll call lists compared to those who obtain work from those lists, Lopez et al.’s statistician states that “[t]he fraction of Hispanic names introduced from the Row [sic] call lists is equal to 0.31.” The fraction of Hispanic names introduced from the roll call lists, however, does not represent the -probability (for purposes of this statistical model) that a Hispanic would have received a referral from that list. The relevant statistic to use as the base for the standard deviation analysis would be the percentage of workers on the lists who were Hispanic. As Lopez et al.’s expert used an incorrect base for the statistical model, the numbers and conclusions flowing from that model are incompetent summary judgment evidence.

Similarly, Lopez et al. used an incorrect base for their statistical analysis of the specific requests by name received by the Union. Concerning that pool of workers, Lopez et al.’s statistician states that “[t]he overall fraction of Hispanic names requested in the Work Call [specific requests] (WC) records is equal to 0.31.” Again, the percentage of Hispanics requested is not the correct base figure. This figure should represent all of the Hispanics who were available and qualified to be called through the specific request exception to the roll call system.

Clearly, the district court’s statement quoted above was uttered by an understandably frustrated court that was struggling to make sense out of a statistical presentation that is simply insusceptible of making sense under the relevant case law or the claims being asserted. The district court 1) considered the percentage of Hispanics who received work through the specific name request method as compared to all workers who received work through that method (26%); 2) compared that to the percéntage of Hispanics who received referrals from the roll call lists as compared to all of the referrals from the roll call lists (23%); and 3) concluded that inasmuch as the former percentage was higher than the latter, the claim of Lopez et al. that maintenance of the specific request system' had a negative effect on Hispanics was an impossibility in the face of their own numbers. The district court’s analysis was a game attempt to interpret Lopez et al.’s befuddled statistics; the gravamen of their claim, after all, was that a negative impact on employment of Hispanic laborers resulted either from the system of specific requests per se or from the way it was being administered by the Union.

What is clear to us and the district court, but apparently not comprehensible (or at least not acceptable) to Lopez et al., is that the statistics generated by their own expert fail to meet the burden of proving a prima facie case. In attempting to prove such a case with statistics, the appellants have failed to use a valid base or starting point and they have improperly mixed their statistical evidence. In simplest terms, Lopez et al. misapprehend the “relevant points of comparison.” In Wards Cove, the Supreme Court reiterated the requirement that when statistical evidence is used in an effort to prove a prima facie case of discrimination, the “proper comparison” must be made “between the qualified persons in the labor market and persons holding at-issue jobs.” As discussed above, Lopez et al. never made — or at least never submitted — a statistical comparison grounded in the correct base figure of qualified Hispanics in the relevant labor market. Instead, they rely for the statistical bases of their different analyses on either 1) the number of Hispanies “introduced from the ro[ll] call list,” or 2) the number of Hispanics for whom requests are made through the specific request exception to the roll call system. Viewed another way, they cherry-picked some of the parts but never considered the whole; they made no effort to provide any statistics from the “relevant labor market.”

As the viability of appellants’ position is totally dependent on the soundness of their statistics, their claims necessarily crumble when the multiple errors of the underlying numbers are exposed.

III

CONCLUSION

That the statistics presented by Lopez et al. were simply and absolutely inadequate to prove a prima facie case of discrimination by the Union is beyond dispute. As a result of our plenary review, we agree with the district court’s grant of summary judgment in favor of the Union. The dismissal of appellants’ action is therefore

AFFIRMED. 
      
      . The international union is involved in this lawsuit because it acted as the administrator of a trusteeship that it had imposed on the local union. The international was administrator during a part of the time period involved in the instant case.
     
      
      . Wards Cove Packing Co. v. Atonio, 490 U.S. 642, 657, 109 S.Ct. 2115, 2124, 104 L.Ed.2d 733 (1989).
     
      
      . Walker v. Sears, Roebuck & Co., 853 F.2d 355, 358 (5th Cir.1988).
     
      
      . 477 U.S. 242, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986).
     
      
      . 477 U.S. 317, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986).
     
      
      . 475 U.S. 574, 106 S.Ct. 1348, 89 L.Ed.2d 538 (1986).
     
      
      . Fed.R.Civ.P. 56(c); see Celotex, 477 U.S. at 323-25, 106 S.Ct. at 2552-53.
     
      
      . Walker, 853 F.2d at 358.
     
      
      . Even a cursory review of the trial court’s record reveals that this assumption is quite generous. Lopez et al.’s expert’s first report was the only one timely filed in accordance with the district court’s discovery schedule. Although it is unclear which reports were considered by the magistrate judge and district court, it is clear that the district court could have refused to consider the late filed summary judgment evidence. See Geiserman v. MacDonald, 893 F.2d 787, 790-91 (5th Cir.1990). Moreover, it is not immediately clear from the documents submitted to the district court that the reports even purport to raise a genuine issue of material fact (i.e., the first report states the disparity between the groups compared therein "is not statistically significant”).
     
      
      . Although the percentage of jobs filled by Hispanics in the second set of statistics (26%) is larger than the percentage of Hispanics who received work in the first set (from "outside” the roll call) (23%), there is a larger standard deviation because there was larger sample group. See infra note 14.
     
      
      . Carroll v. Sears, Roebuck & Co., 708 F.2d 183, 190 (5th Cir.1983) (citing Hazelwood School Dist. v. United States, 433 U.S. 299, 97 S.Ct. 2736, 53 L.Ed.2d 768 (1977)).
     
      
      . Williams v. New Orleans Steamship Ass'n, 673 F.2d 742, 750 n. 13 (5th Cir.1982) (citing Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 1281 n. 17, 51 L.Ed.2d 498 (1977)).
     
      
      . Technically, our statement in Williams is a dictum, and it is not completely supported by the cited case. Williams involved a truly “gross” disparity between the number of African Americans available to work and those working in the gangs — 10.24 standard deviations. The Williams footnote cites the Castaneda opinion in which the "difference between the expected and observed number of Mexican-Americans [was] approximately 29 standard deviations." 430 U.S. at 496 n. 17, 97 S.Ct. at 1281 n. 17. In a footnote in Castaneda, the Supreme Court stated that “[a]s a general rule for such large samples, if the difference between the expected value and the observed value is greater than two or three standard deviations, then the hypothesis that the [selection] was random would be suspect to a social scientist." Id. We think it is doubtful that the Supreme Court's statement supports the ironclad rule, as Lopez et al. assert the statement in Williams to be, that anytime there is a difference of three standard deviations between the expected and observed number a prima fa-cie case has been made out. (For example, the ironclad rule that Lopez et al. assert does not function well in view of the workings of statistical analyses — the persuasiveness of which rise and fall relative to the size of the sample population involved.) Nevertheless, as there are glaring flaws in Lopez et al.’s statistics, we need not reach the issue.
     
      
      .As discussed in the Williams opinion, 673 F.2d at 749 n. 13, the calculation of standard deviations is as follows:
      Number of S/D = O-NP
      NP (l-P)
      S/D = Standard Deviations
      O = Actual number of Hispanics who received a referral in a certain population (roll call or specific request)
      N = Total number of workers in the relevant population (roll call or specific request)
      P = Probability of a Hispanic being called from the relevant population
     
      
      . July 14, 1991 Report.
     
      
      . In addition to Lopez et al.’s improper bases, their analyses are, in the Union’s words, doubly flawed as they improperly intertwine different areas of the workforce being looked at. The first set of statistics purports to compare the "[a]ctual number of Hispanics introduced from outside the RC lists," the "[t]otal number of workers introduced from outside the RC lists,” and the "[probability of a Hispanic worker being introduced from the RC list.” (Emphasis added). A plaintiff simply cannot prove a discrimination case by comparing different parts of the employer’s labor force, see, Wards Cove, 490 U.S. at 657, 109 S.Ct. at 2124 or, in the instant case, referrals given out under the work call and roll call. Similarly, the second statistical model compares the ”[a]ctual number of Hispanics in the TWI records [i.e., worker who received referrals from the roll call lists]," the "[t]otal number of workers in the TWI records,” and the "[probability of a Hispanic worker being requested in a Work Call." Again, the comparison between roll call and non-roll call (i.e., work call) is simply improper.
     
      
      . Wards Cove, 490 U.S. at 657, 109 S.Ct. at 2124.
     
      
      . We note that Lopez et al. also asserts error in the district court’s terse judgment vis-á-vis their disparate treatment claim. We find that the district court has set out all that need be said about Lopez et al.’s summary judgment evidence on this point, and we decline as hopeless the opportunity to elucidate further for the benefit of counsel for Lopez et al.
     