In the HERD research list Ohio U clusters with these schools (all Carnegie R2 like Ohio U, all with R&D budgets of $45-60M)

Alabama-Huntsville, SUNY Binghamton, Maine. Texas-Arlington, Louisiana Lafayette, UMass Lowell, UMBC, ODU, North Dakota, UWM, William & Mary, Ohio U, Montana, Wichita State, Akron, South Dakota State, Cleveland State, SIU-Carbondale, Wyoming

Forbes lumps Ohio U roughly with this group of schools:
Oklahoma State, Georgia State, Montana State, Montana, New Mexico, San Diego State, Maine, Texas-Arlington, Rhode Island, Northern Arizona

It is similar rated but a bit easier to get into than Tennessee, UMBC, UCF, USF, Buffalo, Nebraska, Auburn, UAB

The schools Ohio lists as peers on their fact sheet seem to be "aspirational" rather than true peers:

Colorado State, Iowa State, Oklahoma State, Oregon State, Missouri, New Hampshire, Rhode Island, South Carolina, Utah, West Virginia

These are schools with between 3x and 10x the level of research going on at campus, and includes two AAU schools, and includes 6 flagships which Ohio U is not. Excepting OK State and UNH and RIU they are all R1 schools.

Honestly I can understand OK State, West Virginia, UNH as aspirations. I would suggest Idaho, San Diego State and Georgia State as more realistic peers however. Schools in the middle level tend to list the schools they aspire to be their peers, not their true peers. The best way to look at it is, do the schools you list as peers consider your school a peer? If the answer is no, that they see you as farther down the pecking order, then you list is less truthful than aspirational.