PHOENIX — The conviction that private prisons save money helped drive more than 30 states to turn to them for housing inmates. But Arizona shows that popular wisdom might be wrong: Data there suggest that privately operated prisons can cost more to operate than state-run prisons — even though they often steer clear of the sickest, costliest inmates.

The state’s experience has particular relevance now, as many politicians have promised to ease budget problems by trimming state agencies. Florida and Ohio are planning major shifts toward private prisons, and Arizona is expected to sign deals doubling its private-inmate population.

The measures would be a shot in the arm for an industry that has struggled, in some places, to fill prison beds as the number of inmates nationwide has leveled off. But hopes of big taxpayer benefits might end in disappointment, independent experts say.

“There’s a perception that the private sector is always going to do it more efficiently and less costly,” said Russ Van Vleet, a former co-director of the University of Utah Criminal Justice Center. “But there really isn’t much out there that says that’s correct.”