Wal-Mart store No. 79 looks just like the company’s other “supercenters.” Open 24/7, with some 345 full- and part-time employees, it is a fixture in the heavily blue-collar city of Joplin, Mo. But there is an experiment under way here—one that has potentially far-reaching implications for employment and upward mobility nationwide as the country settles in to enjoy another Labor Day weekend.

Wal-Mart is famous for keeping costs down, including employee-related costs. In Joplin, the company is testing a new approach: investing...