
522 N.W.2d 864 (1994)
James B. BUSH, Plaintiff-Appellant,
v.
The BOARD OF TRUSTEES OF the MUNICIPAL FIRE AND POLICE RETIREMENT SYSTEM OF IOWA, Defendant-Appellee.
No. 93-1415.
Court of Appeals of Iowa.
August 25, 1994.
*865 James Elliott and James P. Walseth of Legal Services Corp. of Iowa, Cedar Rapids, for appellant.
Alice E. Helle and James H. Gilliam of Brown, Winick, Graves, Donnelly, Baskerville & Schoenebaum, P.L.C., Des Moines, for appellee.
Heard by DONIELSON, C.J., and HAYDEN and HABHAB, JJ.
HABHAB, Judge.
The petitioner, James Bush, appeals from a district court ruling dismissing his petition for writ of certiorari. Bush claims the district court erred in that the decision of the Board of the Municipal Fire and Police Retirement System of Iowa ("Board") was not supported by substantial evidence and, therefore, illegal. We affirm.
Bush began working for the Marshalltown Fire Department in March 1982. Approximately two years later Bush became an emergency medical technician. The position required him to respond to accident scenes and medical emergencies where he witnessed some grisly sites.
In February 1991, Bush voluntarily sought treatment at the Marshalltown Medical and Surgery Center after he began suffering suicidal thoughts. He was diagnosed as having a major depressive episode and the center noted he was suffering some degree of stress due to his employment as a emergency medical technician.
In February 1992, Bush again voluntarily sought treatment at the center for cocaine abuse. A report during the treatment for that abuse indicated the possibility of Bush suffering from posttraumatic stress disorder ("PTSD").
*866 On March 16, 1992, Bush sought ordinary disability benefits pursuant to Iowa Code chapter 411 from the Board. He subsequently amended his request to seek accidental disability benefits alleging he was disabled by PTSD arising from his employment. The next day, Bush was involuntarily terminated from employment with the fire department for his failure to pursue treatment and counseling for drug abuse.
On June 10, 1992, the board denied Bush's disability application. Bush appealed and a hearing was held. The Board again denied Bush's disability application.
Thereafter, Bush filed a petition for writ of certiorari challenging the board's decision. The district court dismissed Bush's petition for writ of certiorari. The court concluded the medical board did not certify Bush as being permanently incapacitated and, therefore, Bush was not entitled to accidental disability benefits as a matter of law. The court also concluded the board's decision was supported by substantial evidence indicating there was conflicting information in the medical record concerning the nature and extent of Bush's incapacity and that there was very little evidence indicating permanent incapacity. Bush then filed a notice of appeal.
A right of appeal is not provided by Iowa Code chapter 411 (1991). A party dissatisfied with a decision of the Board may secure judicial review by filing a petition for writ of certiorari. Benson v. Fort Dodge Police Pension Bd., 312 N.W.2d 548, 550 (Iowa 1981). Certiorari may not be used to correct mere errors on the part of the inferior tribunal. Giesey v. Board of Adjustment of Iowa City, 229 N.W.2d 258, 259 (Iowa 1975). Certiorari is an action at law to test the legality of the action taken by an inferior tribunal and our review is not de novo. Bevere v. Kilburg, 326 N.W.2d 902, 904 (Iowa 1982). An illegality is established if the lower body has not acted in accordance with statute or its findings are not supported by substantial evidence. Iowa Freedom of Information Council v. Wifvat, 328 N.W.2d 920, 922 (Iowa 1983). The burden of showing the illegality in the proceedings of the inferior tribunal rests upon the party making the assertion. Carstensen v. Board of Trustees, 253 N.W.2d 560, 562 (Iowa 1977).
Our supreme court has stated the substantial evidence rule used in actions of certiorari is analogous to that used in actions reviewing decisions of administrative agencies. Grant v. Fritz, 201 N.W.2d 188, 195 (Iowa 1972). Evidence is substantial if a reasonable person would find it adequate to reach the given conclusion, even if a reviewing court might draw a contrary inference. Burns v. Board of Nursing, 495 N.W.2d 698, 699 (Iowa 1993). The possibility that two persons might reach differing conclusions upon review of the evidence does not prevent a finding from being supported by substantial evidence. Id. at 197.
Iowa Code section 411.6(3) provides the following criteria for ordinary disability benefits:
Upon application to the system, of a member in service or of the chief of the police or fire departments, respectively, any member shall be retired by the system, not less than thirty and not more than ninety days next following the date of filing the application, on an ordinary disability retirement allowance, if the medical board after a medical examination of the member certifies that the member is mentally or physically incapacitated for further performance of duty, that the incapacity is likely to be permanent, and that the member should be retired.
In addition, as a prerequisite to entitlement to accidental disability benefits, the applicant must prove he is "totally and permanently incapacitated for duty as the nature and proximate result of an injury or disease incurred in or aggravated by the actual performance of duty, at some definite time and place." Iowa Code § 411.6(5).
We find substantial evidence to support the Board's position that Bush had not met the criteria for disability benefits under either section.
Bush received a medical evaluation by three physicians at the University of Iowa Hospitals and Clinics. They did not certify that Bush was permanently disabled. In a psychiatric referral summary, Dr. Bruce *867 Pfohl opined Bush "is unable to function as a firefighter for psychiatric reasons." However, in a diagnostic evaluation, Dr. Pfohl and Dr. Brown stated they could not make a clear diagnosis of PTSD because of Bush's history of drug and alcohol abuse. In addition, the Marshalltown Medical and Surgical Center, in its discharge summary, noted Bush had "no indication of primary depression, psychotic thinking disorder or organicity." The final diagnosis on the report was "cocaine abuse." In its recommendation the center stated Bush's "overall prognosis is good" but "he should not return to work at this time."
Bush claims the Board ignored or did not address the Veterans Administration Medical Center's psychologist, Dr. Lamberty, who concluded Bush suffered from PTSD disabling Bush from working as a firefighter. The weight to be accorded evidence is within the agency's exclusive domain. Burns, 495 N.W.2d at 699.
We find substantial evidence supports the Board's decision. The district court correctly dismissed Bush's petition for writ of certiorari.
AFFIRMED.
