The symbol
d
= denotes equality in distribution, that is equality of the CDFs. The mathematical
notation
d
> denotes stochastic dominance, that is the cumulative distribution
of Scorescient is less than or equal to the CDF of Scoreclass (and the strict inequality
is true for some subsets of ). In other words, under the alternative hypothesis the
scores of candidates coming from scientific studies tend to be distributed on greater
values. The significance level is