This study investigated the correlations between science research group members' perceptions of power bases used by their group (lab, team) leader (coercive, reward, legitimate, expert and referent) and the effect of those perceptions on group members' attitudinal compliance, behavioral compliance, and satisfaction with supervision. Participants were postdoctoral and Ph.D. students at a research institution in the UK that is a world leader in its fields. Three questionnaires, including the Rahim Leader Power Inventory (RLPI), the Compliance with Supervisor's Wishes (CSW), and the satisfaction with supervision facet of the Job Descriptive Index (JDI), were used. The results of statistical descriptive analysis indicated that group members perceived expert power used by the leader as the greatest among five power bases; while the results of the multiple regression analysis indicated legitimate power and expert power were positively related to attitudinal compliance; legitimate power, coercive power and expert power had positive correlations with group members' behavioral compliance; and referent power, reward power, and expert power were positively associated with group members' satisfaction with supervision. Based on the findings, this study offers recommendations for the effective exercising of power in research groups and draws implications for advancing administration in science institutions.