Clark appeals from his conviction for perjury under 18 U.S.C. § 1621 and for making a false statement under 18 U.S.C. § 1001 . Jeffery appeals from her conviction for perjury in violation of 18 U.S.C. § 1621 . The district court had jurisdiction under 18 U.S.C. § 3231 . We have jurisdiction over this timely consolidated appeal pursuant to 28 U.S.C. § 1291 . We affirm.

I

Clark and Jeffery are both Black, roomed together, and served as police officers for the Oakland Police Department (department) during 1983. On July 29, 1983, Clark, Jeffery, and two other police officers filed a grievance with the department, alleging the department’s arrest quota system was unconstitutional. The department dismissed this grievance. On September 5, 1983, Clark filed a similar claim with the Equal Employment Opportunity Commission (EEOC) complaining of illegal quotas, harassment, and undesirable assignments.

A few weeks before filing the EEOC complaint, Clark and Jeffery had violated the department’s sick leave policy. On Sunday, August 14, 1983, Clark and Jeffery called from a roadside telephone, claiming they were sick at home. Because both officers were to begin a vacation the next day, their supervisors became suspicious about a claim they were sick. Attempts to contact Clark and Jeffery revealed that no one was home. When the two officers returned from vacation, they denied being away from home on August 14. They were disciplined for violating the department’s sick leave policy.

On December 12, 1983, Clark filed a second complaint with the EEOC. Clark alleged that the department’s discipline for sick leave abuse was really imposed in retaliation for Clark’s earlier filing of a charge of discrimination with the EEOC. In the second complaint, Clark denied abusing the department’s sick leave policy and asserted that the department had no basis for its disciplinary actions.

In 1985, Clark, Jeffery, and four other officers filed a civil rights lawsuit against the City of Oakland and some of its employees, including members of the department. They alleged that these members of the department had discriminated against them and had committed “numerous retaliatory acts” after they had filed the original complaint with the EEOC. Sergeant Jones, Clark and Jeffery’s supervisor at the time of the sick leave incident, was named as a defendant. The complaint alleged that Jones had harassed the plaintiffs because of their opposition to the department’s quota system. The city filed an answer to the complaint, denying the allegations of discrimination and asserting that any disciplinary actions taken against the plaintiffs were justified by the plaintiffs’ violations of department policies.

Discovery in connection with the civil rights lawsuit began in 1986. At an early deposition, Clark and Jeffery’s lawyer questioned Jones about his handling of the sick leave incident. The sick leave incident was also raised in the depositions of Clark and Jeffery; both categorically denied abusing the department’s sick leave policy. Clark also acknowledged that in a pending civil service case he had alleged that the sick leave incident was part of his claim of harassment in the civil rights lawsuit.

After the depositions of Clark and Jeffery, the city’s attorney obtained Jeffery’s telephone records and driving record. The telephone records revealed that the calls made to the police department on August 14, 1983, had been placed from two cities in Iowa. In addition, the driving records showed that Jeffery had received a speeding ticket in Nevada on August 13, 1983, and another in Iowa on August 14, 1983. Based on this information, both officers were charged with perjury under 18 U.S.C. § 1621 and with conspiracy to commit perjury under 18 U.S.C. § 371 . Clark was also charged with making a false statement to an agency under 18 U.S.C. § 1001 .

During trial, the judge ruled that for purposes of the prosecution under 18 U.S.C. § 1621 , the deposition testimony of Clark and Jeffery concerning the sick leave incident was material to the civil rights litigation. The jury found Clark and Jeffery guilty and the judge sentenced both to three years in prison, but suspended their sentences and put them on probation. As a condition of probation the judge ordered Clark and Jeffery each to publish an apology in the local newspaper and in the police department’s newsletter. The required apology, composed by the district judge, stated:

Clark and Jeffery raise four issues on appeal. They first argue that the judge should have permitted the jury to decide whether the false statements were material under section 1621. Second, they argue that there was insufficient evidence to support the judge’s ruling that the statements were material. Third, they contend that the judge erred by excluding evidence related to EEOC procedures. Finally, they argue that the conditions of probation violated the first amendment.

II

A lie is not perjurious unless it concerns a “material matter.” 18 U.S.C. § 1621 . The Supreme Court has ruled that materiality is an issue of law for the court to decide. Sinclair v. United States, 279 U.S. 263, 298 , 49 S.Ct. 268, 273 , 73 L.Ed. 692 (1929).

Sinclair should end the argument. But Clark and Jeffery contend that we should rule that materiality is an issue of fact for the jury. They suggest that Sinclair is “out dated precedent” and that permitting a judge to determine materiality conflicts with the right to trial by jury and with the burden of proof beyond a reasonable doubt. Finally, Clark and Jeffery point out that under a different perjury statute, 18 U.S.C. § 1001 , we have declined to follow the majority approach and have instead permitted the question of materiality to be decided by the jury. United States v. Valdez, 594 F.2d 725, 729 (9th Cir.1979) {Valdez).

Sinclair is not “out dated precedent.” The Supreme Court recently cited Sinclair with approval when considering the materiality issue in a different context. In Kungys v. United States, 485 U.S. 759 , 108 S.Ct. 1537 , 99 L.Ed.2d 839 (1988) {Kungys), the Court examined materiality in conjunction with a denaturalization proceeding under 8 U.S.C. § 1451 (a). The Court ruled that under section 1451, materiality should be decided by the judge as a matter of law. Id. at 772 , 108 S.Ct. at 1547 . The Court relied on Sinclair and perjury cases by the courts of appeals following it. Id. Fur thermore, the Court identified a rationale of general applicability which directs the judge to decide materiality in the perjury cases:

Id., quoting United States v. Abadi, 706 F.2d 178, 180 (6th Cir.), cert. denied, 464 U.S. 821 , 104 S.Ct. 86 , 78 L.Ed.2d 95 (1983).

Although Kungys did not involve a criminal proceeding, its reliance on Sinclair demonstrates that Sinclair is still authoritative. Moreover, the reasoning of Kun-gys provides an additional reason for our conclusion. Because materiality must be determined by reference to the underlying substantive law, it involves a legal question which should be resolved by the judge.

Our Valdez decision does not compel us to reach a different conclusion. In Valdez , we held that materiality under 18 U.S.C. § 1001 should be determined by the jury. Valdez, 594 F.2d at 729 . The materiality issue was submitted to the jury in the section 1001 count in this case. However, we have twice declined to extend that rule to other statutes. United States v. Flake, 746 F.2d 535, 537-38 (9th Cir.1984) (Flake), cert. denied, 469 U.S. 1225 , 105 S.Ct. 1220 , 84 L.Ed.2d 360 (1985); United States v. Larm, 824 F.2d 780, 783-84 (9th Cir.1987), cert. denied, 484 U.S. 1078 , 108 S.Ct. 1057 , 98 L.Ed.2d 1019 (1988). In doing so, we explicitly stated that as a general rule, materiality in a perjury case should be determined by the judge. Flake, 746 F.2d at 537-38 .

We are bound to follow our previous cases and those of the Supreme Court. We therefore reject Clark and Jeffery’s argument that the judge erred by ruling on materiality as a matter of law in the section 1621 counts.

Ill

Clark and Jeffery next argue that the judge erred by concluding that their false statements were material to the civil rights litigation. Since materiality is a question of law, it must be reviewed de novo. United States v. Martinez, 855 F.2d 621, 623 (9th Cir.1988).

A statement is material “if it ‘has a natural tendency to influence, or was capable of influencing, the decision of’ the decisionmaking body to which it was addressed.” Kungys, 485 U.S. at 770 , 108 S.Ct. at 1546 , quoting Weinstock v. United States, 231 F.2d 699, 701-02 (D.C.Cir.1956); see also United States v. Lococo, 450 F.2d 1196, 1199 (9th Cir.1971) (Lococo) (under 18 U.S.C. § 1621 , a statement is material if it “tends to influence the grand jury”), cert. denied, 406 U.S. 945 , 92 S.Ct. 2040 , 32 L.Ed.2d 331 (1972). Under this test, a material false statement is one which “is relevant to any subsidiary issue under consideration.” Lococo, 450 F.2d at 1199 .

The district judge did not err in concluding that the false statements concerning the sick leave incident would have a “tendency to influence” the resolution of issues in the civil rights litigation. The civil rights complaint makes numerous references to the department’s “retaliatory and discriminatory policies.” The introductory section of the complaint states that “Plaintiffs Theresa Jeffery [and] John Clark ... filed formal complaints with the Equal Employment Opportunities [sic] Commission. The filing of the complaint was followed by numerous retaliatory acts.... ” The complaint designates as a separate claim the plaintiffs’ “right to be free from retaliatory employment practices” and seeks damages as compensation for the “retaliatory policies and practices of defendants.”

The testimony about the sick leave incident was relevant to the issue of whether the department committed “retaliatory employment practices.” Jones disciplined Clark and Jeffery for the sick leave abuse during the period of time they alleged that Jones was harassing them for filing the EEOC complaint. The sick leave discipline is the most well-documented, and perhaps the only, discipline imposed during this time period. Certainly knowing that Clark and Jeffery were not actually sick would have “a tendency to influence” the jury’s decision whether this particular disciplinary action was imposed for harassment and retaliation. In addition, the existence of a legitimate explanation for one of the department’s actions would support the department’s claim that other disciplinary actions were justified.

Our conclusion that the sick leave incident was material to the harassment claim is supported by the deposition testimony of Clark: he admitted that he had earlier stated that the sick leave discipline was part of the harassment claim. Furthermore, the attorney who represented the city in the civil rights litigation testified that the plaintiffs’ lawyer specifically told him that the sick leave incident was a part of the lawsuit. Although Clark and Jeffery now argue that this testimony was not credible, we will not review a judge’s credibility determinations unless clearly erroneous. See United States v. McConney, 728 F.2d 1195, 1201 (9th Cir.) (en banc) (judge is in better position than appellate court to make credibility determinations), cert. denied, 469 U.S. 824 , 105 S.Ct. 101 , 83 L.Ed.2d 46 (1984). There was no clear error in relying on this testimony.

IV

Clark next argues that his conviction under 18 U.S.C. § 1001 should be reversed because the judge improperly excluded testimony about the EEOC’s method of processing grievances. Clark argues that the excluded evidence was relevant to his defense. However, we do not reach this argument because the error was not properly preserved for appeal.

Under the Federal Rules of Evidence, exclusion of evidence is appealable only if “the substance of the evidence was made known to the court by offer or was apparent from the context.” Fed.R.Evid. 103(a); see also United States v. Bagley, 837 F.2d 371, 375 (9th Cir.) (“To preserve an issue for review requires an offer of proof and the making of a record.”), cert. denied, 488 U.S. 924 , 109 S.Ct. 304 , 102 L.Ed.2d 323 (1988). When the appellant has failed to make an offer of proof, evidentiary rulings will be reviewed only when they are “plain errors affecting substantial rights.” Fed. R.Evid. 103(d). Plain error is found only in exceptional circumstances. United States v. Kessi, 868 F.2d 1097, 1102 (9th Cir.1989).

Clark does not argue that the judge’s evidentiary ruling was plain error. Rather he suggests that he made an offer of proof when the issue of the admissibility of the EEOC evidence was initially raised. We do not find this contention verified by the record. It is true that Clark’s lawyer made general statements to the judge concerning the scope of evidence he wanted to present. However, the judge made no evidentiary ruling at that time. Clark’s argument, which did not discuss the testimony of specific witnesses, was not an offer of proof.

Clark also contends he made an offer of proof at the time the EEOC testimony was excluded. Because it is not in the record, Clark suggests this may have taken place during an off the record discussion. We are not free to consider evidence outside of the record. See Andersen v. Cumming, 827 F.2d 1303, 1305 (9th Cir.1987) (appealing litigant must ensure that sufficient facts are developed at trial to support a challenge on appeal). There is no offer of proof in the record, and therefore we cannot consider this evidentiary issue on appeal.

V

Clark and Jeffery finally challenge one of the conditions of probation: that they each publish a public apology. They argue that the probation condition violates their first amendment right to refrain from speaking. See Wooley v. Maynard, 430 U.S. 705, 714 , 97 S.Ct. 1428, 1435 , 51 L.Ed.2d 752 (1977). We review conditions of probation for an abuse of discretion. United States v. Consuelo-Gonzalez, 521 F.2d 259, 264 (9th Cir.1975) (Consuelo-Gonzalez ).

The test for validity of probation conditions, even where preferred rights are affected, is “whether the limitations are primarily designed to affect the rehabilitation of the probationer or insure the protection of the public.” Id. at 265, n. 14 . To apply this test, our court “must determine whether the sentencing judge imposed the conditions for permissible purposes, and then it must determine whether the conditions are reasonably related to the purposes.” United States v. Terrigno, 838 F.2d 371, 374 (9th Cir.1988). “[T]he standard for determining the reasonable relationship between probation conditions and the purposes of probation is necessarily very flexible precisely because ‘of our uncertainty about how rehabilitation is accomplished.’ ” Id., quoting Consuelo-Gonzalez, 521 F.2d at 264 .

The condition of probation imposed here meets this test. The record supports the conclusion that the judge imposed the requirement of a public apology for rehabilitation. Neither Clark nor Jeffery have admitted guilt or taken responsibility for their actions. Therefore, a public apology may serve a rehabilitative purpose. See Gollaher v. United States, 419 F.2d 520, 530 (9th Cir.) (“It is almost axiomatic that the first step toward rehabilitation of an offender is the offender’s recognition that he was at fault.”), cert. denied, 396 U.S. 960 , 90 S.Ct. 434 , 24 L.Ed.2d 424 (1969). Because the probation condition was reasonably related to the permissible end of rehabilitation, requiring it was not an abuse of discretion.

AFFIRMED.