For t-test, if samples are normally distributed, t-test is accurate even for small sample size. For large sample size, because of the central limit theorem, t-test is also accurate. This is the reason t-test is a 'robust' method. According to John, there is not general theory on why a method is robust or not, because it depend on how the method will be used. John said that reliability is in the field of operational research.
Tianwei suggest that binned sample may not be uniformally distributed, so a taking the center may add a 'bias' to the rounding procedure.
For the Emory biostat program, GRE verbal is required over 50%, and quantitative part is over 80%. Their experience is that GRE score is the best predictor of student performance in the program, especially the quantitative score.
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