The results were very different from those of the controlled trial.

If we look only at the intervention group as an observational trial, it appears that people who didn’t make use of the program went to the campus gym 3.8 days per year, and those who participated in it went 7.4 times per year. Based on that, the program appears to be a success. But when the intervention group is compared with the control group as a randomized controlled trial, the differences disappear. Those in the control group went 5.9 times per year, and those in the intervention group went 5.8 times per year.

Researchers looked at whether people participated in a race, like a marathon, a 10-kilometer run or a five-kilometer run. The observational analysis, comparing nonparticipants with participants, showed a significant difference in running: 3.3 percent of people versus 9.2 percent. The randomized controlled trial, on the other hand, found 6.5 percent versus 6 percent.

Wellness programs sometimes claim to save money by reducing health care spending. The observational analysis supports this belief. It found that participants spent significantly less than nonparticipants on health care ($525 versus $657) and on hospital-related costs ($273 versus $387). The randomized controlled trial showed that the wellness program had little effect on spending compared with the control group in both overall spending ($576 versus $568) and hospital spending ($317 versus $297).

The researchers even looked at the percentage of people who left their job for any reason. In the observational analysis, 15.4 percent of nonparticipants did so compared with only 7.2 percent of participants. It appears from such an analysis that wellness programs are associated with retaining workers. But the randomized controlled trial showed that no such causal link exists, as 12 percent of the control group exited the job, compared with 10.8 percent of the intervention group.

Why such stark differences? “The most likely explanation is that participants differ from nonparticipants in very important ways,” said Julian Reif, one of the study’s principal investigators. “Therefore, when a wellness program is offered, the differences seen between those who take advantage of it and those who don’t are due to differences in the people rather than differences from the program.”

Often, the best we can do for an observational trial is to try to adjust — control, researchers say — for variables we can measure and that might also affect the results. These researchers did. In one analysis, they controlled for sex, age, race, salary and status as faculty or staff. They still found that the results of the observational analysis were significant for all the outcomes discussed above. In an even more heavily controlled analysis, they used machine learning to decide whether to control for even more variables, including (but not limited to) past health, smoking and drinking status; pre-intervention exercise; medication use; and sick days taken.

The differences were unchanged.

“If we had published only these observational analyses, the headline result could have been that even after controlling for a battery of confounding variables, participation in a wellness program was associated with a significant reduction in health care spending, an improvement in exercise, and a lower chance of ceasing employment,” said David Molitor, another principal investigator of the study.