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Leshno and Levy (2002) extend stochastic dominance (SD) theory to almost stochastic dominance (ASD) for {\\it most} decision makers. When comparing any two prospects, Guo, et al.\\ (2013) find that there will be ASD relationship even there is only very little difference in mean, variance, skewness, or kurtosis. Investors may prefer to conclude ASD only if the dominance is nearly almost. Levy, et al. (2010) have provided two approaches to solve the problem. In this paper, we extend their work by first recommending an existing stochastic dominance test to handle the issue and thereafter developing a new test for the ASD which could detect dominance for any pre-determined small value. We also provide two approaches to obtain the critical values for our proposed test.
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