A Large-Sample Test of the Hypothesis that one of two Random Variables is Stochastically Larger than the Other

  title={A Large-Sample Test of the Hypothesis that one of two Random Variables is Stochastically Larger than the Other},
  author={A. W. Marshall},
  journal={Journal of the American Statistical Association},
  • A. W. Marshall
  • Published 1 September 1951
  • Mathematics
  • Journal of the American Statistical Association
T HIS paper presents a large-sample, non-parametric test using grouped data. It applies when x and y are random variables with continuous cumulative distribution functions (c.d.f.'s) F(x) and G(y). A statistic S based upon the sum of the differences, at selected points, of the two sample c.d.f.'s, Fm*(x) and GQn*(y), is proposed for testing the hypothesis F(a) G(a) for every a against alternative hypotheses in which one of two variables is stochastically larger than the other. A variable x is… 
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