From 1976 to 1994, F. Donald Bush was employed by Dictaphone Corporation, a maker of office equipment. In January of 1993, when Bush was 46 years old, he was demoted from his executive-level position, and two years later was terminated. Bush sued Dictaphone based on the Age Discrimination in Employment Act (“ADEA”), 29 U.S.C. §§ 621-634, the prohibitions on sex discrimination contained in Title VII of the Civil Rights Act of 1964, 42 U.S.C. §§ 2000e to 2000e-17, and various state law claims.
The district court granted Dictaphone’s motion for summary judgment. On appeal, Bush claims that the district court erred (1) in denying Bush’s motion to suppress certain statements as hearsay, (2) in curtailing Bush’s ability to depose two corporate officers of Dictaphone’s corporate parent, and (3) in granting Dictaphone’s motion for summary judgment. For the reasons set forth below, we AFFIRM the decision of the district court.
I. BACKGROUND
The facts in this case are largely undisputed. Bush began working for Dictaphone in 1976. In 1979, Dictaphone promoted him to “Region Sales Manager,” a position later known as “Region Vice-President.” In the early and mid-1980s, his performance reviews were generally quite positive, and he was recognized by the company for good performance on several occasions. In 1989, after Bush began reporting to the Vice-President of Sales for the Communication Recording Systems Division, a woman, things began to change.
In February and March of 1992, the Sales Vice President became dissatisfied with Bush for two reasons. First, Bush responded to one of her routine business inquiries in an insubordinate and confrontational manner. Second, sales associates that Bush supervised claimed that he was abusive, unpredictable, and had a tendency to “fly off the handle.” Bush was counseled by his superiors, and given an opportunity to correct his behavior. Because he did not, he was demoted ten months later to a lower position.
One year after his demotion, in early 1994, Bush’s supervisors began receiving complaints that certain employees who worked for Bush were afraid that he might become violent. This caused Dictaphone to convene a “Prevention of Critical Incidents” team, a corporate structure created to prevent potential acts of workplace violence. The team required Bush, under threat of termination, to be evaluated by a psychiatrist named Howard Sokolov. After examining Bush, Dr. Sokolov concluded:
[I]n a practical sense, he probably can not function [as a salesman] in the context of a corporate employee at Dictaphone____ [I]t is extremely likely he will wage a war of vituperation, legal complaints, obstructionism, and pestering to attempt to win *366against the corporation and salvage some self esteem.
As part of the same evaluation process, Bush was also examined by psychologist Marlene Koean, who stated that “Because of his high levels of underlying hostility and some suggestion that he may act on his hostility, caution should be exercised in dealing with this man.” The team offered Bush the opportunity to be evaluated by a mental health professional of his own choosing, at company expense. He declined to do so. Based on the psychological and psychiatric assessments, as well as the team’s own review of Bush’s record, the team recommended that Bush be terminated. Dictaphone acted on the team’s recommendation by discharging him in June of 1994. Shortly thereafter, Bush filed the instant lawsuit.
Bush concedes most of the foregoing facts, but contends that Dictaphone’s allegations were a pretext designed to mask its discrimination against him based on his age and gender. Bush alleges that he was replaced by a younger woman when he was demoted, and by a younger man when he was terminated. Bush also claims to have heard the Sales Vice President make derogatory comments toward older people, although the only example he gave was a single alleged reference by her to “greybeards.” Bush also claims that a number of older men were forced out of their jobs in favor of younger employees.
In the district court, Bush moved to strike a number of statements contained in declarations offered by Dictaphone. These statements consisted of information that the Sales Vice President and other Dictaphone supervisors received from employees supervised by Bush. Bush claimed in his motion that these statements should have been excluded as inadmissible hearsay. The district court denied the motion, finding that the statements were not offered for the truth of the matter asserted.
Bush also sought to compel the depositions of two high-ranking executives of Pitney-Bowes, Dictaphone’s corporate parent. He alleged that because these two executives were in charge of Bush’s division, they must have information relating to Bush’s discharge. The district court allowed only a limited deposition of the President and Chief Operating Officer, and refused to allow the deposition of the Chief Executive Officer.
Ultimately, the district court rejected all of Bush’s substantive claims, granting summary judgment for Dictaphone. Bush now appeals.
II. ANALYSIS
A. Failure to Comply with Appellate Rules
As a preliminary matter, Dictaphone claims in its brief that Bush’s appeal should be dismissed because his statement of facts failed to cite to the record, a violation of Rule 28 of the Federal Rules of Appellate Procedure and Sixth Circuit Rule 10. In support of this claim, Dictaphone cites two Ninth Circuit cases, Mitchel v. General Electric Co., 689 F.2d 877 (9th Cir.1982), and N/S Gorp. v. Liberty Mutual Insurance Co., 127 F.3d 1145 (9th Cir.1997), and a case from this circuit decided in 1903, Mitchell Transportation Co. v. Green, 120 F. 49, 60-61 (6th Cir.1903) (per curiam).
A review of those cases, however, indicates that dismissal is appropriate only when a brief is so inadequate that a court cannot interpret it at all. See, e.g., Mitchel, 689 F.2d at 878-79. In addition, the appellants in the cited eases were given a chance to correct their errors and failed to do so. In contrast, Bush’s reply brief contains a statement of facts that is in full compliance with the appellate rules. His appeal will therefore not be dismissed on this basis.
B. Admission of Alleged Hearsay
Bush moved under Rule 56(e) of the Federal Rules of Civil Procedure to strike significant portions of four different declarations offered by Dictaphone. Each declaration stated that the declarant, a corporate decision-maker, had been told by unidentified co-workers that Bush was abusive or unstable. For example, one secretary complained that Bush had “gone off the deep end” and another Dictaphone employee stated that he would no longer permit Bush to have contact *367with his family. Bush claimed that these averments were inadmissible hearsay under Rule 802 of the Federal Rules of Evidence. In the same order in which it granted summary judgment, the district court denied Bush’s motion. The district court found that the statements were not being offered to prove the truth of the matter asserted (i.e., that Bush was an abusive boss), but “were admissible for the limited purpose of considering the grounds upon which the declarants based their decisions with regard to the employment status of the plaintiff.”
This court reviews de novo a trial court’s hearsay determinations under the Federal Rules of Evidence. See Hancock v. Dodson, 958 F.2d 1367, 1371 (6th Cir.1992) (stating that although a district court’s evi-dentiary determinations are generally reviewed for an abuse of discretion, a district court’s determination that proffered evidence is hearsay within the meaning of the Federal Rules of Evidence is a conclusion of law subject to de novo review). Evidence is hearsay only when the out-of-court statement is offered to prove the truth of the matter asserted. See Fed.R.Evid. 801(c).
In this case, the truth of the statements is not at issue as long as the declarants had a reasonable basis to believe them to be true. See United States v. Martin, 897 F.2d 1368, 1371 (6th Cir.1990) (holding that testimony based upon an out-of-court statement of an unnamed declarant, indicating that defendant was charged with food stamp trafficking, was not hearsay because it was offered for the limited purpose of explaining how and why the investigation of the defendant began). Because Bush does not challenge the declar-ants’ reasonable basis to believe that the statements were true, the hearsay rule is inapplicable and the district court’s decision was proper.
C. Order Limiting Depositions
Bush complains that the district court erred by limiting his ability to depose two senior officers of Pitney-Bowes, Dictaphone’s then corporate parent. In a separate one-page order dated some four months before the court entered summary judgment, the magistrate judge limited Bush’s deposition of Marc Breslawsky, the President and Chief Operating Officer of Pitney-Bowes, to two hours, and further limited the deposition to questions regarding “ageist statements allegedly made by him and his involvement, if any, in plaintiffs demotion or termination.” The magistrate judge also denied Bush’s motion to depose George Harvey, the Chief Executive Officer of Pitney-Bowes.
“The scope of discovery is, of course, within the broad discretion of the trial court---- An order denying further discovery will be grounds for reversal only if it was an abuse of discretion resulting in substantial prejudice.” Lewis v. ACB Bus. Servs., Inc., 135 F.3d 389, 402 (6th Cir.1998) (internal quotation marks and citation omitted).
The record in this ease contains no direct evidence that either Breslawsky or Harvey had any involvement in Bush’s termination. Bush’s brief alleges that they were aware of his situation, and that Breslawsky had made certain “ageist” remarks; namely, that Bres-lawsky had described some of Dictaphone’s older employees as “old men” and “old farts” on at least one occasion. He does not allege, however, and the record does not contain, any evidence that these men even knew that Bush had been terminated, much less that they in some way caused it. Neither does the record contain any evidence that they were involved in a pattern or practice of age discrimination. Under the circumstances, the limitations imposed by the magistrate judge seem a reasonable way to balance Bush’s right to discovery with the need to prevent “fishing expeditions.”
Bush does not cite a single ease that supports his contention that limiting discovery under these circumstances constituted reversible error, nor does he explain how he was substantially prejudiced under the standard articulated in Lewis. As a result, we hold that the district court did not abuse its discretion in limiting the scope of discovery.
D. Summary Judgment
1. Standard of Review
This court reviews de novo a grant of summary judgment. See Terry Barr *368Sales Agency, Inc. v. All-Lock Co., 96 F.3d 174, 178 (6th Cir.1996). The district court’s ruling should be affirmed if there are no genuine issues of material fact and the moving party is entitled to judgment as a matter of law. See Fed.R.Civ.P. 56(c); Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 250, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986). All evidence and inferences must be construed in the light most favorable to the non-moving party. See United States v. Diebold, Inc., 369 U.S. 654, 655, 82 S.Ct. 993, 8 L.Ed.2d 176 (1962).
2. Age Discrimination
Claims under the ADEA are typically analyzed within the framework set forth in McDonnell Douglas Corp. v. Green, 477 U.S. 792, 802-03, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973) (explaining the burden-shifting format). See O’Connor v. Consol. Coin Caterers Corp., 517 U.S. 308, 310-13, 116 S.Ct. 1307, 134 L.Ed.2d 433 (1996) (modifying the McDonnell Douglas framework for an ADEA case). Under the modified McDonnell Douglas framework, a plaintiff first must establish a prima facie case by showing that (1) he was at least 40 years old at the time of the alleged discrimination, (2) he was subjected to an adverse employment action, (3) he was otherwise qualified for the position, and (4) the successful applicant was substantially younger than the plaintiff. See Barnett v. Department of Veterans Affairs, 153 F.3d 338, 341 (6th Cir.1998). If the plaintiff establishes a prima facie case, the burden of production then shifts to the defendant to produce evidence of a non-discriminatory reason for its action. See Barnett, 153 F.3d at 341. If the defendant can come forth with such a reason, the burden returns to the plaintiff to demonstrate that the defendant’s proffered reason is pretextual. See id.
a. Bush’s Prima Facie Case
The district court found that Bush easily satisfied the first two factors; i.e., Bush was within the protected class because of his age, and he was both demoted and terminated, each of which is clearly an adverse employment action. The district court also found, without explanation, that Bush was “otherwise qualified” for the job he held. This court has not addressed the precise requirements for satisfying this third factor, and we decline to do so here. A manager who makes the employees under his supervision fear for their safety could be said to be unqualified. We will assume without deciding, however, that Bush’s long tenure with Dictaphone is sufficient to show that he was “otherwise qualified.”
Assuming that Bush met the first three prongs of the McDonnell Douglas test, he was then required to show that he was replaced by someone “substantially younger.” When Bush was demoted, he was replaced by a woman less than five years younger, who was herself more than forty years old. The district court held that such a small age gap did not meet the “substantially younger” standard. In the absence of any proof to the contrary, we agree that no reasonable jury could find that Bush’s 41 year old replacement was “substantially younger” than Bush (then 46 years old). As a result, with regard to his demotion, Bush failed to make out a prima facie claim under McDonnell Douglas.
On the other hand, when Bush was finally terminated, he was replaced by a 32 year old man. This is sufficient to meet the fourth prong of the test. Bush thus established a prima facie case of age discrimination based on his termination.
b. Dictaphone’s Legitimate, Norn-Discriminatory Explanation
Because Bush made out a prima facie claim, Dictaphone was required to show a legitimate, non-discriminatory reason for the discharge. See Barnett, 153 F.3d at 341. Dictaphone met this burden by relying on the professional judgments of a psychiatrist and a psychologist, both of whom concluded that Bush was not fit to continue in his position. The psychologist, Dr. Kocan, specifically recommended that “caution” be exercised in dealing with him. Bush does not dispute that Dictaphone gave him every chance to challenge these findings, even offering to pay for an examination with a psychologist or psychiatrist of Bush’s own choosing. But Bush chose not to avail himself of *369that opportunity. The findings of Drs. Ko-can and Sokolov are therefore unchallenged in the record. Dictaphone has therefore met its burden of showing a legitimate, non-discriminatory reason for the discharge.
c. Bush’s Shouiing of Pretext
Once the employer has presented a legitimate, non-discriminatory reason for the discharge, the plaintiff must show that the proffered reason is pretextual. See Barnett, 153 F.3d at 341. In an attempt to do so, Bush relies on the affidavit of a psychiatrist, Dr. Gerlaeh, who Bush retained. Dr. Ger-lach’s affidavit, however, does not materially advance Bush’s case. As the district court noted, Bush does not allege that Dictaphone had access to Dr. Gerlach’s opinion when it made its decision to terminate him. As a result, Dr. Gerlach’s affidavit is immaterial to the establishment of pretext, and Bush is left to rely on his own unsupported allegations.
Dr. Gerlaeh asserted that Drs. Sokolov and Kocan misdiagnosed Bush. But even if Dr. Gerlach’s opinion had been found persuasive, it would not have resurrected Bush’s claim, because the only proof Bush offered to establish pretext was a number of alleged “ageist” comments made by certain Dictaphone officials. Bush, however, presented no proof that anyone connected with the decisions to demote or terminate him made any such age-based comments. “[Statements by nondecisionmakers, or statements by decisionmakers unrelated to the decisional process itself [can not] suffice to satisfy the plaintiffs burden ...” of demonstrating animus. Price Waterhouse v. Hopkins, 490 U.S. 228, 277, 109 S.Ct. 1775, 104 L.Ed.2d 268 (1989) (O’Connor, J., concurring). The adverse employment decisions regarding Bush were made by David Nassef, the corporate ombudsman, and the Prevention of Critical Incidents team. Bush does not allege that discriminatory comments were made by any of these people. The comments he relies on, therefore, do not establish a material issue of fact for trial.
In addition, Bush’s brief lists some twenty-five instances of Dictaphone’s conduct that he claims support his case. These instances generally involved certain older employees who were allegedly terminated or forced to retire, allegedly discriminatory comments made by company officials who had nothing to do with Bush’s termination, or alleged conduct by Bush’s supervisors that was either remote in time or of unarticulated relevance. Having carefully reviewed each of these allegations, we find that none of them, either individually or collectively, are sufficient to establish a material issue of fact for trial. Without discussing each of Bush’s allegations in detail, suffice it to say that they are either too vague to be actionable, not relevant under controlling law, or too remote in time to support Bush’s claims. Taking every factual inference in the light most favorable to Bush, as we must, Bush’s allegations are insufficient to establish a cause of action. The district court’s decision was, therefore, correct.
d. Direct Evidence of Discrimination
Bush also attempts to avail himself of an exception to the requirements of the burden-shifting analysis. This analysis, as set forth in McDonnell Douglas, is designed to assure that the “plaintiff [has] his day in court despite the unavailability of direct evidence.” Loeb v. Textron, Inc., 600 F.2d 1003, 1014 (1st Cir.1979). But the McDonnell Douglas test is inapplicable when the plaintiff presents direct evidence of discrimination. See International Brotherhood of Teamsters v. United States, 431 U.S. 324, 358, n. 44, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977) (holding that “[t]he importance of McDonnell Douglas lies, not in its specification of the discrete elements of proof there required, but in its recognition of the general principle that any Title VII plaintiff must carry the initial burden of offering evidence adequate to create an inference that an employment decision was based on a discriminatory criterion illegal under the Act”).
Bush makes much of this exception in his brief, arguing that the district court erred because, under Ohio law, direct evidence is “a method of proof, not a type of evidence.” Mauzy v. Kelly Servs., Inc., 75 Ohio St.3d 578, 664 N.E.2d 1272, 1279 (Ohio 1996) (holding that a plaintiff may establish a pñma facie case of age discrimination by presenting *370evidence, of any nature, to show that an employer was motivated by discriminatory intent). Under this standard, he argues that he has met his burden of going forward.
Bush is correct with regard to Ohio’s definition of direct evidence. The Sixth Circuit, however, has taken the opposite approach. See Manzer v. Diamond Shamrock Chemicals Co., 29 F.3d 1078, 1081 (6th Cir.1994) (holding that evidence that would require the jury to infer a fact is not direct evidence); see also Schlett v. Avco Fin. Servs.,Inc., 950 F.Supp. 823, 828 (N.D.Ohio 1996) (holding that “direct evidence is found, for instance, where an employer’s policy is discriminatory on its face or where a statement by an employer directly shows there is a discriminatory motive.”).
But even under Ohio law, “irrespective of which method is utilized to establish discriminatory intent, plaintiff must show that she was discharged on account of age.” Mauzy, 664 N.E.2d at 1280 (emphasis and internal quotation marks omitted). In other words, even if direct evidence allows a plaintiff to escape the burden-shifting approach, the plaintiff still bears the burden of persuasion that age was the cause of the adverse employment action. This Bush has failed to do.
3. Sex Discrimination
Bush also claims that his demotion and termination were illegally based on his sex. In support of this claim, Bush offered evidence that both he and his secretary, Marjorie Johnson, had seen a memorandum from the Sales Vice President directing that only females be hired for open management positions, that Bush had twice rebuffed her sexual advances, and that a younger man with whom the Sales Vice President had allegedly had a sexual relationship was promoted despite the fact that he was unqualified.
Although such evidence might potentially raise a genuine issue of material fact regarding a sex discrimination claim, we find that in this ease there exist several impediments to Bush’s allegations. In the first place, the district court noted that Bush had failed to even address his claim of sex discrimination in his motion in opposition to summary judgment. Second, the alleged memorandum about hiring only females was not introduced into evidence, and in any event did not indicate any discrimination against existing employees. Finally, Bush’s sex discrimination claim fails for the same reasons that his age discrimination claim fails, i.e., even if he had made out a prima facie claim under McDonnell Douglas, he failed to show that Dictaphone’s proffered non-discriminatory reason for discharging him was pretextual. The district court’s grant of summary judgment on Bush’s sex discrimination claim was therefore proper.
J. Breach of Contract, Promissory Estop-pel, Intentional Infliction of Emotional Distress, Retaliation, Fraud, and Invasion of Privacy
Bush does not pursue any of these claims on appeal, and they are therefore waived See Kocsis v. Multi-Care Mgmt., Inc., 97 F.3d 876, 881 (6th Cir.1996) (holding that arguments not raised in the brief on appeal are deemed waived). See also United States v. Elder, 90 F.3d 1110, 1118 (6th Cir.1996) (holding that issues raised by an appellant in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived.)
III. CONCLUSION
For all of the reasons set forth above, we AFFIRM the decision of the district court.