Attorney General Martha Coakley announced Wednesday plans to shed light on how executives at major nonprofits earn compensation, saying she will begin by homing in on how major Massachusetts health care organizations pay their leaders. “While it is not the role of this office to set compensation levels, we are entrusted with the responsibility to assure that governance practice in this area is open, transparent and for the exclusive benefit of our charitable organizations and the public they serve,” Coakley said in a statement. Blue Cross Blue Shield of Massachusetts, Fallon Health Plan, Harvard Pilgrim Health Plan, and Tufts Health Plan will be the subject of Coakley’s initial effort, which will also include an examination of how they pay board directors, who often go uncompensated at smaller nonprofits. Eventually, other sectors may be included in her examination, according to the statement. The investigation will be conducted by Coakley’s Non-Profit Organizations/Public Charities Division. “The basis for compensation has not, to the Division’s knowledge, ever been clearly articulated to the public and we are asking each of the current boards to take a fresh look at the practice,” the division’s chief, David Spackman, wrote to the health care organizations in a memo issued Wednesday. “If the practice is to continue at any of them, it should do so only on the basis of a sound and well considered foundation, for which the benefits and risks have been fully explored and appropriately considered, and in a manner in which the independence of the board has been preserved.” The division also made an overture to the organizations, noting that the effort should “not be construed as an attempt to substitute the judgment of the Division for that of committed, knowledgeable and diligent boards.” “The most expensive mistake an organization can make is to place the wrong person at the helm or the wrong people in the board room,” Spackman wrote.