BOGGS, Circuit Judge.

Three plaintiffs brought actions under 42 U.S.C. § 1981 and § 1983 against the city of Akron and members of its Civil Service Commission, alleging that they had been terminated from police officer cadet training because of their race. On cross motions for summary judgment, the district court granted summary judgment against plaintiffs and they appealed to this court. We affirm the district court.

I

Garrick Black, Joseph M. Smith, and Pamela Benson, black citizens of the United States, were terminated from the police cadet training program of the City of Akron after passing the Civil Service written examination for qualification as a police officer. They were given a physical stress test by the City, which they did not pass. They now contend that summary judgment was improper because they received individual physical performance examinations from their own physicians and passed those tests, and because the City's tests was incorrectly administered by a non-physician.

The City of Akron established the physical test requirement prior to the appellants' applications to the force, in an attempt to dispense with the bona fide occupational requirement of age for police officers. The City measured physical performance data for at least 340 police officers already on the force and compiled the requirements from the results of the test. The study that resulted, entitled "Construction and Validation of a Police Officer Physical Fitness Battery as a Substitute for Minimum Age Requirements," occupies 88 pages in the appendix, and cites legal precedent for the city's use of bona fide occupational requirements. It is co-authored by Dr. Richard A. Mostardi, a Ph.D. in exercise physiology, whose administration of the physical performance test is challenged by the appellants. Dr. Mostardi's affidavit submitted on behalf of the motion for summary judgment, and his testimony before the Civil Service Commission, set forth additional facts verifying the study.

The Civil Service Commission of the City of Akron adopted the medical standards resulting from the study as the entrance requirement for police officers on January 6, 1983. In August 1983, the position of police officer was posted. Appellants responded to the notice and passed the Civil Service portion of the examination. On March 23, 1984, the district court ordered the City of Akron to hire at least forty applicants, in the ratio of two blacks for every three whites, to remedy the effects of past discrimination.

Appellants were given the same stress test by Dr. Mostardi as were all other applicants, consisting of a musculoskeletal test (CYBEX), and a cardiovascular test. The reasons for the disqualifications of the appellants are contained in Dr. Mostardi's testimony before the Civil Service Commission of the City of Akron. Mostardi gave all participants pass-fail grades. Only three white applicants and three black applicants failed the test, out of a total of 42 white applicants and 33 black applicants.

After appellants were removed from the eligibility list for police officer candidates, they asked for and received a hearing in the administrative process on the denial of eligibility. The denial was affirmed. Next, they contacted their own physicians for equivalent performance tests given by Dr. Melvin Farris. Dr. Ormand, a cardiologist, stated that Benson had no heart abnormalities. This was confirmed by the examination of another cardiologist, Dr. Battistelli. Black was also examined by Battistelli, who tested him using the Bruce Protocol and rated his exercise capacity as "very good." Dr. Polley also gave Black a good cardiological rating. Smith's cholesterol count was evaluated by Dr. Polley and rated very good.

At oral argument, appellants stated that Benson and Smith were reinstated to the police academy training program and had been hired as police officers, because they later passed the physical examination that they did not pass the first time. They still seek back pay and an earlier seniority date. Garrick Black, who also retook the examination, was again rejected, and his claim for reinstatement is still viable.

II

On a motion for summary judgment, the movant has the burden of showing conclusively that there exists no genuine issue of material fact. The evidence, together with all inferences to be drawn therefrom, must be read in the light most favorable to the party opposing the motion. Smith v. Hudson, 600 F.2d 60, 63 (6th Cir.), cert. dismissed, 444 U.S. 986, 100 S.Ct. 45, 62 L.Ed.2d 415 (1979). Furthermore, the district court is obliged to consider not only the materials specifically offered for support of the motion, but also all pleadings, depositions, answers to interrogatories, and admissions properly on file and before the court. Smith, 600 F.2d at 64.

A prima facie case of discrimination under 42 U.S.C. § 1983 is demonstrated by (1) deprivation of rights under the federal constitution or other laws, and (2) action under color of state law. Day v. Wayne County Board of Auditors, 749 F.2d 1199 (6th Cir. 1984). This court has not previously addressed the propriety of statistical proof in actions under 42 U.S.C. § 1983. In disparate impact actions under Title VII, statistics are admissible to prove a prima facie case of race discrimination. McDonnell Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973). The Supreme Court has said that:

Statistics showing racial or ethnic imbalance are probative . . . only because such imbalance is often a telltale sign of purposeful discrimination; absent explanation, it is ordinarily to be expected that nondiscriminatory hiring practices will in time result in a work force more or less representative of the racial and ethnic composition of the population in the community from which employees are hired.

Teamsters v. United States, 431 U.S. 324, 339 n. 20 at 340, 97 S.Ct. 1843, 1856 n. 20 at 1857, 52 L.Ed.2d 396 (1977).

In the interest of considering all of the probative evidence, we hold today that statistical proof may be used in actions under 42 U.S.C. § 1983; and furthermore, that cases and regulations promulgated under Title VII furnish useful guides to the interpretation of this statute. See Tagupa v. Board of Directors, 633 F.2d 1309, 1312 (9th Cir. 1980).

In this action under §§ 1981 and 1983, which attacks racially neutral employment practices, plaintiffs must demonstrate some purpose to discriminate by a state actor. General Building Contractors Ass'n. v. Pennsylvania, 458 U.S. 375, 390, 102 S.Ct. 3141, 3149, 73 L.Ed.2d 835 (1982); Personnel Adm'r. of Massachusetts v. Feeney, 442 U.S. 256, 284, 99 S.Ct. 2282, 2299, 60 L.Ed.2d 870 (1979); See also Washington v. Davis, 426 U.S. 229, 240, 96 S.Ct. 2040, 2047, 48 L.Ed.2d 597 (1976). Evidence of adverse impact of a challenged practice alone is not sufficient to sustain an action under these sections, as it could be under Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000 et seq. (1982). However, such allegations of statistical evidence of an adverse impact might be sufficient to survive summary judgment.

In this case, as the court below noted, there was no evidence sufficient to survive summary judgment that plaintiffs, taken individually, were qualified applicants so as to make a prima facie case of discrimination. While plaintiffs did allege that they were rated as satisfactory on tests which they procured, they presented no evidence to offset the city's affidavits as to the relevance of the physical stress test given here, or the manner of administration (other than an unsupported attack on Mostardi's qualifications and the development of the test). Thus, the only remaining means by which plaintiffs could avoid summary judgment is the application of statistical evidence, specifically the "four/fifths" (4/5) rule promulgated by the EEOC.

III

The district court reasoned that a prima facie case of discriminatory intent had not been established under the 4/5 rule, set forth in the EEOC's Uniform Guidelines on Employee Selection Procedures, 29 C.F.R. § 1607.4D (1987):

A selection rate for any race . . . which is less than four-fifths (4/5) (or eighty percent) of the rate for the group with the highest rate will generally be regarded by the Federal enforcement agencies as evidence of adverse impact, while a greater than four-fifths rate will generally not be regarded . . . as evidence of adverse impact.

Three of the black applicants failed the test and three of the white applicants failed the test, or 9% and 7% of those who took the test. The ratio of selection rates of blacks and whites, .91/.93, is much more than 4/5. Plaintiffs attack this application of the four-fifths rule as both per se misleading and wrongly applied. They contend that the ratio of the rejection rates should be considered rather than the ratio of selection rates, and in this case, that the smallness of the sample in this case should obviate the use of the rule altogether.

In this case the plaintiffs have both issues exactly backwards. The 4/5 rule, by its own clear words, applies to selection rates, not rejection rates. This is because the selection rate is the statistic which is important to the applicants and which best measures the likely motivations of the employer. If, for a very competitive job, an employer chose 5% of the white applicants but only 1% of the black applicants, this significant disparity would flunk the 4/5 test based upon selection rates. Based upon rejection rates, however, the employer would pass with flying colors, as he rejected almost everyone who applied, and the 95% rate for white applicants is quite close to the 99% rate for black applicants.

In addition, using rejection rates makes very little sense when, as here, most applicants are passing the tests. If every white passed a particular test, it would then be a violation of the rule to reject any black, because 0 (the white rejection rate) divided by any black rejection rate, no matter how small, is still 0, and thus less than 4/5. The court below was correct to focus on the relative selection rates, which were well within the 4/5 rule.

Next, plaintiffs are correct that the 4/5 rule has been criticized when used in the context of a small sample of employees being tested. However, that criticism has been of the rule's usefulness as an affirmative indicator of discrimination in those circumstances. See Fudge v. City of Providence Fire Dept., 766 F.2d 650, 658 n. 10. (1st Cir. 1985). The concurring opinion in Fudge focuses on the sample problem in a meaningful way. The difficulty discussed there is that a discrimination whose existence is indicated by the 4/5 rule is much more likely to be real in the event of a large sample than a small sample. Thus, if an employer selects 60% of the blacks and 80% of the whites, this very likely indicates a real difference in selection procedures if he is choosing 600 blacks out of 1,000 and 800 whites out of 1,000. On the other hand, if he chooses 3 blacks out of 5 applicants and 4 whites out of 5 applicants, both common sense and rigorous statistical analysis tell us that it is much more likely that mere chance is the controlling factor. Thus, the small size of the sample might be a reason to rule that there was no prima facie case even if the 4/5 rule were violated, but it is certainly not a reason for finding a prima facie case when the 4/5 rule is not violated.

Finally, we note in passing the following peculiarity of the application of the 4/5 rule in this circumstance of a small sample with most applicants of both races passing. If we first ignore the race of the applicants, we note that 6 out of 75 failed the test. When we analyze the racial impact, we realize that each of the six rejected applicants must have been of some race, and that racial division must occur by whole numbers. Partial people do not pass or fail tests. Thus, by plaintiffs' theory of comparison of rejection rates, there is absolutely no way to reject six people out of this sample and avoid a prima facie case of discrimination.

The actual division of the six rejected (three blacks and three whites) is most nearly consistent with the racial composition of the pool tested. If the six failures were to have been four of one race and two of another, plaintiffs' theory would lead to a much stronger showing of adverse impact against one race or the other than the actual result permits. Thus, even if any sensible inferences could be drawn from a small number of rejections out of a small sample, the pattern of the six rejections here was the most nearly fair that was possible in a statistical sense. Plaintiffs cannot allege or infer any adverse impact suggestive of discrimination from these figures. The court below was thus correct in granting summary judgment despite plaintiffs' statistical efforts, and we AFFIRM its decision.