Either one works, but because 'groups' is plural, 'efforts' might be better. Basically, it depends on whether the writer is thinking about many individual efforts of different sorts, or of a general effort to solve the problem. '
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It should be efforts.Because the sentence is talking about continued attempts.
This: Employees’ group membership is likely to moderate diversity incentives’ effect on their pre-promotion efforts. Or this: Employees’ group membership is likely to moderate diversity incentives’ effect on their pre-promotion effort.