Second-order　stochastic　dominance　plays　an　important　role　in　reliability　and　various　branches　of　economics　such　as　finance　and　decision-making　under　risk,　and　statistical　testing　for　the　stochastic　dominance　is　often　useful　in　practice.　In　this　paper,　we　present　a　test　of　stochastic　equality　under　the　constraint　of　second-order　stochastic　dominance　based　on　the　theory　of　empirical　processes.　The　asymptotic　distribution　of　the　test　statistic　is　obtained,　and　a　simple　method　to　compute　the　critical　value　is　derived.　Simulation　results　and　real　data　examples　are　presented　to　illustrate　the　proposed　test　method.