OPINION OF THE COURT
STAPLETON, Circuit Judge:
This case brings before us the controversial subject of polygraph testing. The district court held the use of the polygraph for pre-employment screening by the police and correctional departments of the City of Philadelphia to be a violation of the due process and equal protection rights of the plaintiffs. 668 F.Supp. 441. Because we conclude that the polygraph requirement does not violate the plaintiffs’ constitutional rights, we will reverse.
I.
Pennsylvania law forbids the use of polygraph testing for pre-employment screening by any private or public employer, with a few specific exceptions; among the exceptions are public law enforcement agencies. The relevant section of the Pennsylvania statutes, 18 Pa.Cons.Stat.Ann. § 7321 (Purdon 1983 & 1987 Supp.), reads:
(a) Offense defined. — A person is guilty of a misdemeanor of the second degree if he requires as a condition for employment or continuation of employment that an employee or other individual shall take a polygraph test or any form of a mechanical or electrical lie detector test.
(b) Exception. — The provisions of subsection (a) of this section shall not apply to employees or other individuals in the field of public law enforcement or who dispense or have access to narcotics or dangerous drugs.
As permitted by state law, the police and prison departments of the City of Philadelphia have chosen to make polygraph testing an element of their hiring procedures. The plaintiffs in this case are unsuccessful applicants for employment as City police officers or correctional officers. The reason for the plaintiffs’ lack of success in obtaining the employment they sought is their disqualification from consideration for such employment upon their failure to pass the polygraph test.
Like other public agencies, the City law enforcement departments base their hiring on the results of a competitive civil service examination conducted pursuant to 4 Pa. Code § 95 et seq.; individuals passing this test are placed on a certified eligibility list. As openings occur in the police and prison departments, individuals high up on the certified eligibility lists for positions in those departments are notified. Each notified individual must then pass a number of additional tests before being found qualified for employment by the hiring department. The additional tests required by the police and prison departments include a medical examination, a psychiatric examination, a background investigation, and, usually last in the process, a polygraph test.
The background investigation includes completion of a Personal Data Questionnaire (PDQ), which contains questions [1218]*1218about family and financial status, driving record, educational and employment history, criminal record, use of alcoholic beverages, and use, sale, and possession of illicit drugs. Before candidates come in to fill out the PDQ and to have their initial background investigation interview, they are notified in writing of the content of the PDQ, including the questions relating to illicit drugs, and are informed that they will have to take a polygraph test that will cover the PDQ questions on their use, possession, and sale of illicit drugs.1 Candidates are also informed that deception or falsification in answering PDQ/polygraph questions may result in rejection. Applicants may defer taking the polygraph test, if they wish, or may request to be reconsidered at a later time. The police and prison departments will hire otherwise qualified individuals who admit to having used or possessed drugs over six months before completing the PDQ and taking the polygraph.
The polygraph testing procedures currently used by both the police and prison departments were developed in 1983 in the course of settling class actions by blacks and Hispanics who had brought suit alleging that the Philadelphia Police Department’s hiring and promotion policies were discriminatory. See Commonwealth of Pennsylvania v. O’Neill, 100 F.R.D. 354 (E.D.Pa.1983), aff'd without opinion 746 F.2d 1465 (3d Cir.1984); Alvarez v. City of Philadelphia, 98 F.R.D. 286 (E.D.Pa.1983). These settlements require the above-described prior notification concerning the PDQ/polygraph questions, and require that if during the test the polygraph examiner finds the applicant “deceptive”, the applicant must be told immediately and given a chance to explain, deny, or admit the deception. If the applicant denies being deceptive, or if the explanation is found unsatisfactory by the examiner, the applicant must have the opportunity to retake the test with a second examiner. The second examiner does not review the results of the first prior to readministering the polygraph. If the second examiner finds no deception, the applicant is considered to have passed; if the second examiner also finds the applicant deceptive, that finding is ordinarily final and preclusive of employment. The applicant may, however, appeal to either the Police Department’s Review Panel or to the Superintendent of Prisons or the prison review panel, and the reviewers may decide to give the applicant the opportunity to take a third test. If the applicant is found deceptive on a third test, he or she will not be hired. Deception is found on about half of all the tests given.
During a pre-test interview, applicants are asked if there is any other information they would like to provide. During a post-test review, if deception is indicated, they are asked again if there is any information they are withholding. Admissions to disqualifying information were made during these interviews by 315 of the 1028 applicants for positions with the Police Department in 1985, and 251 of the 619 applicants in 1986.
According to Police Commissioner Tucker, an applicant must pass the polygraph test in order to be hired by the Philadelphia Police Department. Prison Superintendent Owens has stated that if an individual could convince the prison review panel that the polygraph was unfair, he or she might be hired by the prison department notwithstanding failure of the polygraph. In no case has an applicant who failed to pass a polygraph test been hired by either of the departments. The results of the tests are not made public, but are used only within the departments for evaluating the suitability of the applicant for employment.
There is considerable controversy about the validity and reliability of polygraph testing. The polygraph measures stress or anxiety, which in many cases may not correlate very well with deception. In 1983, Congress’ Office of Technology Assessment put out a Technical Memorandum on [1219]*1219polygraph testing, which read in part as follows:
There are two major reasons why an overall measure of validity is not possible. First, the polygraph test is, in reality, a very complex process that is much more than the instrument. Although the instrument is essentially the same for all applications, the types of individuals tested, training of the examiner, purpose of the test, and types of questions asked, among other factors, can differ substantially. A polygraph test requires that the examiner infer deception or truthfulness based on a comparison of the person’s physiological responses to various questions.... Second, the research on polygraph validity varies widely in terms of not only results, but also in the quality of research design and methodology. Thus, conclusions about scientific validity can be made only in the context of specific applications and even then must be tempered by the limitations of available research evidence.
OTA concluded that the available research evidence does not establish the scientific validity of the polygraph test for personnel security screening.
[D]espite many decades of judicial, legislative, and scientific discussion, no consensus has emerged about the accuracy of polygraph tests.
App. at 618, 652. Professor Leonard Saxe, who headed the OTA group, testified as an expert witness for the plaintiffs. According to Professor Saxe, polygraph tests are likely to find many truthful applicants deceptive (false positives) and some unknown lesser, though “potentially large”, number of deceptive applicants truthful (false negatives). App. at 344. When polygraphs are used for pre-employment screening, the risk of false positive results is generally thought to be higher than that of false negative results.
The City’s law enforcement departments consider polygraph tests reliable and valid. An additional advantage of using the polygraph test, in the departments’ view, is that it encourages applicants to be candid in responding to questions on the PDQ. The departments do not believe that this secondary advantage can be separated from the trustworthiness that they consider to be the main advantage of the polygraph. Both advantages, the departments believe, enable them to acquire necessary information about potential employees.
The departments do admit that polygraph testing is not perfect. While they recognize the impossibility of conducting error-free polygraph testing, however, they correctly point out that there is no evidence establishing that the polygraph is not valid. Moreover, they point out that there must be some method of acquiring the information necessary to make choices among applicants and stress that the decision to utilize a polygraph examination must be evaluated in light of the available alternatives. The departments’ expert, Dr. Frank Hor-vath, noted that
there is also little scientific support for many of the procedures which are used in employment screening. There is little “scientific” evidence, for instance, to show that background investigations actually yield accurate information or that psychiatric interviews accurately discriminate between “good” and “bad” candidates. On the other hand, there is considerable scientific data to show that personal interviews as generally used in employment screening are unreliable; yet, employers continue to carry out such interviews. Written psychological tests, moreover, have received considerable research attention which, according to many, shows little scientific support for their use.
App. at 398.
The plaintiffs claim that use of the polygraph test results to deny them employment deprives them of their constitutional rights to procedural and substantive due process and equal protection of law.2 Af[1220]*1220ter a bench trial, the district court held in favor of the plaintiffs.
On appeal, the defendants contend that no protected property or liberty interest of the plaintiffs was at stake, and thus the plaintiffs cannot maintain a procedural due process claim. They also argue that the use of the polygraph by the departments has a rational basis, and so passes muster under the applicable standards of equal protection and substantive due process analysis.3 We review de novo the district court’s choice, interpretation, and application of legal principles, and review for clear error the findings of fact made by the district court. Mims v. Shapp, 744 F.2d 946, 949 (3d Cir.1984).
II.
In Board of Regents v. Roth, the Supreme Court made it clear that “[t]he requirements of procedural due process apply only to the deprivation of interests encompassed by the Fourteenth Amendment’s protection of liberty and property.” 408 U.S. 564, 569, 92 S.Ct. 2701, 2705, 33 L.Ed.2d 548 (1972). According to the Court, “to determine whether due process requirements apply in the first place, we must look ... to the nature of the interest at stake.” Id. at 571, 92 S.Ct. at 2706. In this case, the plaintiffs have alleged that they have been deprived of both property and liberty interests by the City departments’ use of the polygraph test to disqualify them from employment.
A. Property Interest
In Roth, the Court explained that
[t]he Fourteenth Amendment’s procedural protection of property is a safeguard of the security of interests that a person has already acquired in specific benefits.... [T]o have a property interest in a benefit, a person clearly must have more than an abstract need or desire for it. He must have more than a unilateral expectation of it. He must, instead, have a legitimate claim of entitlement to it.
Property interests ... are created and their dimensions are defined by existing rules and understandings that stem from an independent source such as state law —rules or understandings that secure certain benefits and that support claims of entitlement to those benefits.
408 U.S. at 576-77, 92 S.Ct. at 2708-09. See also Bishop v. Wood, 426 U.S. 341, 344, 96 S.Ct. 2074, 2077, 48 L.Ed.2d 684 (1976) (no property or liberty interest in public employment exists unless such an interest is created by state law or similar independent source). To demonstrate a property interest, therefore, these plaintiffs must show that under Pennsylvania law they had a legitimate claim of entitlement to employment as City police or prison officers.
The plaintiffs here were never more than applicants for employment by the City. Although the plaintiffs occupied high positions on the civil service eligibility lists for the type of employment they sought, occupancy of these positions entitled the plaintiffs to nothing more than consideration for employment when openings occurred. In Stana v. School Dist. of Pittsburgh, 775 F.2d 122 (3d Cir.1985), we found that there had been a violation of the procedural due [1221]*1221process rights of a school teacher who had been removed from the certified eligibility list on the basis of a negative recommendation, without notice to her or an opportunity for her to be heard. We said:
It is evident that remaining on the eligibility list, which was a prerequisite to a teaching position, was a “legitimate entitlement” that the School District had created through the policies it promulgated to implement the state statute on teacher hiring. As such, it represented both an existing policy or rule and an explicit understanding sufficient to constitute a property interest ... which triggered the requirement for an inquiry that comported with procedural due process.
775 F.2d at 128-27. In this case, unlike Stana, the plaintiffs received the consideration to which they were entitled by reason of their status on the eligibility list.
While the departments were bound to consider the plaintiffs for employment, they were by no means bound to hire the plaintiffs. The plaintiffs can cite to no section of the Pennsylvania statutes which sets an objective standard for the hiring or rejection of applicants from the eligibility lists, and which might thereby create a legitimate claim of entitlement to employment. On the contrary, under the state law applicable here, agencies such as the defendant departments may and do exercise broad discretion in hiring.4 Under these circumstances, there can be no tenable claim of entitlement to employment. See Robb v. City of Philadelphia, 733 F.2d 286, 292-93 (3d Cir.1984) (although Pennsylvania law provides public employees with a limited right to continued employment, such employees have no legitimate claim of entitlement either to continued employment on the same job or to promotion, because those involve discretionary decisions of supervisors); Burns v. Sullivan, 619 F.2d 99, 104 (1st Cir.1980), cert. denied 449 U.S. 893, 101 S.Ct. 256, 66 L.Ed. 2d 121 (where promotions are, under state law, based in part on discretionary judgments of high city officials, no property interest in a promotion can exist). See also Perri v. Aytch, 724 F.2d 362, 364 (3d Cir.1983) (probationary employee of the Court of Common Pleas was dismissed without a hearing after her arrest on a later withdrawn drug-related charge; as the applicable regulations guaranteed that she would be dismissed for just cause only, she had a legitimate claim to a property interest in continued employment and was entitled to a due process hearing). For the same reason, nothing in the departmental hiring practices can be said to create any legitimate claim of entitlement to employment; those practices too involve considerable discretionary decisionmaking.
In sum, we find nothing in the departmental hiring practices or in Pennsylvania law that establishes a legitimate claim of entitlement to employment in applicants like the plaintiffs. We therefore conclude that the plaintiffs’ interest in the civil service positions they sought did not rise to the level of a property interest protected by the Constitution.
2. Liberty Interest
On the subject of liberty interests in employment, this court has stated that
[a]n employment action implicates a fourteenth amendment liberty interest only if it (1) is based on a “charge against [the individual] that might seriously damage his standing and associations in the community ... for example, [by implying] that he had been guilty of dishonesty, or immorality,” or (2) “impose[s] on him a stigma of other disability that forecloses [1222]*1222his freedom to take advantage of other employment opportunities.”
Robb, 733 F.2d at 294 (citing Roth, 408 U.S. at 573, 92 S.Ct. at 2707). We have also held that to state a valid claim of a protected liberty interest, “a plaintiff must plead that the allegedly stigmatizing information was ‘published’ or otherwise disseminated by his government employer to the public.” Chabal v. Reagan, 841 F.2d 1216, 1223 (3d Cir.1988) (citing Bishop v. Wood, 426 U.S. 341, 348, 96 S.Ct. 2074, 2079, 48 L.Ed.2d 684 (1976)); see also Cleveland Bd. of Educ. v. Loudermill, 470 U.S. 532, 547 n. 13, 105 S.Ct. 1487, 1496 n. 13, 84 L.Ed.2d 494 (1985) (failure to allege publication of reasons for dismissal dooms claim of unconstitutional deprivation of liberty interest); Stana, 775 F.2d at 125 n. 1 (though removal from an eligibility list for reasons other than objective test scores could be viewed as reflecting adversely on the character of the person affected and could thus implicate the liberty interest in following a chosen profession, where a plaintiff has not alleged publication, she may not claim deprivation of a liberty interest).
In this case, plaintiffs assert that they have been “branded as liars” on account of their failure to pass the polygraph examination. While the polygraph results might conceivably be viewed as stigmatizing the plaintiffs or damaging their reputations, the plaintiffs have not alleged that any of their polygraph test results were made public. Rather, the departments’ assertion that the polygraph results are kept confidential and undisclosed stands unchallenged. Given that, we find untenable the plaintiffs’ claim that they have been deprived of a liberty interest.5
We conclude that the City’s polygraph requirement does not violate the plaintiffs’ right to procedural due process,6 since no protected property or liberty interest of the plaintiffs is at stake.7
III.
We next address the plaintiffs’ argument that they have been denied equal protection of the law. The plaintiffs rightly refrain from contending that their equal protection claim is entitled to strict or heightened scrutiny; accordingly, we will apply the “general rule ... that legislation is presumed to be valid and will be sustained if the classification drawn by the statute is rationally related to a legitimate state interest.” City of Cleburne v. Cleburne Living Center, Inc., 473 U.S. 432, 439-40, 105 S.Ct. 3249, 3254, 87 L.Ed.2d 313 (1985).8 See Massachusetts Bd. of Retirement v. Murgia, 427 U.S. 307, 313, 96 S.Ct. 2562, 2566-67, 49 L.Ed.2d 520 (1976) (holding rational basis standard appropriate for analyzing claim of unconstitutional deprivation of public employment, where no fundamental right or suspect class is concerned); see also United Bldg. & Constr. Trades Council of Camden v. Mayor of Camden, 465 U.S. 208, 219, 104 S.Ct. 1020, 1028, 79 L.Ed.2d 249 (1984) (stating that “there is no fundamental right to government employment for purposes of the [1223]*1223Equal Protection Clause”). The plaintiffs bear the burden of proof on this issue, and so must show that the requirements imposed by law or regulation “so lack rationality that they constitute a constitutionally impermissible denial of equal protection.” Rogin v. Bensalem Township, 616 F.2d 680, 688 (3d Cir.1980), cert. denied 450 U.S. 1029, 101 S.Ct. 1737, 68 L.Ed.2d 223 (1981). In considering this issue, we bear in mind the Court’s statement that a statute or regulation should not be overturned on equal protection grounds “unless the varying treatment of different groups or persons is so unrelated to the achievement of any combination of legitimate purposes that we can only conclude that the legislature’s actions were irrational.” Vance v. Bradley, 440 U.S. 93, 97, 99 S.Ct. 939, 943, 59 L.Ed.2d 171 (1979).
The defendants stress, and the plaintiffs acknowledge, that the public has a legitimate and, indeed, compelling interest in hiring applicants who are qualified for employment as public law enforcement officers. It is this interest that the polygraph requirement is said to serve. The key question we confront here, therefore, is whether the requirement that applicants pass a polygraph test can arguably be said to result in a better-qualified group of new employees. The defendant City departments need not show that the polygraph requirement does in fact result in the selection of better-qualified group of new employees. Rather, the burden is on the plaintiff applicants to show that the departments’ use of the polygraph could not reasonably be believed to produce a better-qualified group of new hires than would be chosen absent the polygraph requirement.
It is clear that the district court placed the burden on the wrong party in this case, since a necessary stepping-stone to that court’s holding was its conclusion that “[t]he testimony, exhibits and evidence presented at the trial failed to prove the reliability of polygraph tests in general.” App. at 706, 709. The normal remedy for an error of this sort is, of course, for this court to reverse the judgment and remand for application of the correct standard by the district court. However, we conclude that the record requires an affirmative answer to the key question stated above, and thus mandates reversal of the district court’s holding and the entry of judgment for the defendants.
Professor Saxe’s testimony supports the proposition that the validity and reliability of polygraph testing as a device to screen prospective employees have not been scientifically established. It does not demonstrate, however, that it is irrational to believe that the polygraph has utility in connection with the selection of law enforcement officers. First, Professor Saxe acknowledges that “virtually no research has been conducted on the validity of polygraph tests to screen prospective employees,” App. at 354, and it is, accordingly, apparent that such testing has not been empirically established as invalid or unreliable. Moreover, Professor Saxe does not dispute that preemployment polygraph screening is widely used by intelligence and law enforcement agencies which consider it useful in eliminating unqualified candidates. The record indicates that such screening is used by the National Security Administration, the Central Intelligence Agency, and approximately 50% of police departments throughout the nation. Finally, Professor Saxe does not dispute Dr. Horvath’s assertion that “both proponents and opponents maintain that such testing can distinguish between truthful and deceptive persons with an accuracy greater than chance.” App. at 394.
The main flaw of polygraph testing in the employment screening context, overex-clusiveness through generation of false positive results, is not a problem of constitutional significance where, as here, the test of constitutionality is whether the relative quality of the final group selected might possibly be higher than that of the group selected if the polygraph were not used. As we have noted, the public interest that the polygraph allegedly serves is the hiring of persons qualified to be law enforcement officers. The equal protection issue is whether plaintiffs have shown there is no rational basis for believing that the polygraph requirement serves this pur[1224]*1224pose. Thus, in this context, the selected population is the appropriate focus and the fact that other qualified candidates may-have been erroneously excluded from that population is not legally relevant.9
The false negatives that may result from polygraph testing are a more serious problem. If someone who falsely denies being on drugs is not excluded by the polygraph, this obviously has an impact on the selected population. But the appropriate comparison for equal protection purposes is between the results of the evaluation process with the polygraph and the results of the evaluation process without it. If applicants registering false negatives would be selected in the absence of the polygraph, its use occasions no adverse impact on the goal sought to be achieved. Thus, there is a potential for adverse impact only to the extent the departments, if they did not rely on polygraph testing, might adopt alternative procedures that would be more effective in identifying unsuitable candidates. As Dr. Horvath put it,
the important practical issue is not whether polygraph testing is 95% or 90% or even 70% accurate but whether relative to other methods it yields a reasonable degree of accuracy and whether there is another more suitable method of accomplishing the same objective.
App. at 397. The record in this case provides no basis for concluding that superior alternatives are available.10
Finally, we think it rational for the departments to believe that the polygraph requirement results in fuller, more candid disclosures on the PDQ and thus provides additional information that is helpful in selecting qualified law enforcement officers.
In sum, from the plaintiffs’ perspective, the most that can be said on the basis of this record is that the utility of polygraph testing in the preemployment screening of candidates for law enforcement positions is a debatable and much-debated issue. In such situations, legislators and administrators are free to exercise their judgment [1225]*1225regarding the manner in which the public interest will best be served. Ginsberg v. New York, 390 U.S. 629, 642-43, 88 S.Ct. 1274, 1282, 20 L.Ed.2d 195 (1968) (where causal link between pornography and impaired ethical and moral development of youth is debatable, courts “do not demand of legislatures ‘scientifically certain criteria of legislation’ ” and will not overturn the legislative judgment). Accordingly, we conclude that in the absence of a scientific consensus, reasonable law enforcement administrators may choose to include a polygraph requirement in their hiring process without offending the equal protection clause.
The foregoing evaluation of the record evidence supports the polygraph requirement not only against the equal protection challenge, but also against the plaintiffs’ claims of a substantive due process violation, since in analyzing the latter we “defer to the legislative judgment unless it can have no rational, legitimate foundation.” Pace Resources Inc. v. Shrewsbury Township, 808 F.2d 1023, 1037 (3d Cir.1987), cert. denied, — U.S.-, 107 S.Ct. 2482, 96 L.Ed.2d 375 (1987). We therefore hold that the polygraph requirement does not constitute a violation of the plaintiffs’ constitutional rights to equal protection or substantive due process.
IV.
For the foregoing reasons, we reverse the judgment of the district court and remand with instructions that judgment be entered for the defendants.