When Americans and Canadians of European descent began to study Iroquois customs in the 18th and 19th centuries , they found that women assumed a position in Iroquois society that was about equal in power to that of the men . When Americans and Canadians of European descent began to study Iroquois customs in the 18th and 19th centuries , they observed that women assumed a position in Iroquois society roughly equal in power to that of the men .