Do American workers dig wellness initiatives? It’s tough to say.

About a third of U.S. employees surveyed by the Washington, D.C.-based American Psychological Association say they participate in employer-sponsored programs that encourage physical fitness, sound nutrition, and others healthy living initiatives aimed at making workers healthier. Slightly more — 41 percent — said their organization helps employees develop or maintain a healthy lifestyle.

It’s hard to know how to interpret the fact that so few workers believe their employer takes steps to promote their physical well-being. The survey did not query employees on whether they believed it was the role of their employer to assume the role of a health coach.

A far larger percentage of employees — 68 percent — said they were satisfied with the “health and safety practices” of their organization and roughly the same percentage said they believe their employer values the health of employees.

Seventy-three percent of employees who see their managers engaged in well-being initiatives say that their employer helps them pursue healthy lifestyles, while only 11 percent of those who did not perceive such involvement from management say the same.

“Promoting employee well-being isn’t a singular activity, but is instead set up in a climate that is cultivated, embraced and supported by high-level leaders and managers,” says David W. Ballard, director of APA’s Center for Organizational Excellence. “When supervisors’ actions match their words, employees notice.”

Whether employees believe their leaders take an active role in promoting their well-being also likely mirrors their general feelings towards their job and employer. Unsurprisingly, many Americans feel undervalued by their bosses.

Only 50 percent say they are satisfied with the “employee recognition practices” of their employer. The same percentage feel they are adequately compensated and just under half believe that employee recognition is based on a fair assessment system. Just over half say their employee values work-life balance.

Employers should recognize, the study authors say, that wellness initiatives do not necessarily create a sense of well-being among workers.

“Many employers say they focus on workplace wellness, but what is put into place is too often individual programs or policies that aren’t supported by the organization’s culture,” says Ballard. “Employers who truly embrace well-being as part of how they do business create a workplace where both employees and the organization thrive.”