We extend the standard hiring discrimination measure by including the cases where several candidates are invited to the same interview. The new measure considers the order in which the employer will contact the candidates as opposed to considering only whether or not a job applicant is invited to an interview - a practice common in the previous literature. We propose to apply the first order stochastic dominance (FOSD) criterion to the ranking of the candidates, which appears to be especially relevant for hiring discrimination. We show theoretically that FOSD always implies a positive value for the standard discrimination coefficient used in the literature, and that the converse is false. We apply our analysis to a correspondence testing that has been conducted in the Paris region. We sent 8 fictitious candidates with a Master's degree to the same 310 job offers in computing in order to measure gender and origin discrimination. We found that - out of 28 possible comparisons - there are 25 cases of stochastic dominance that we interpret as strong discrimination against some candidates. In our application, the standard discrimination coefficient tends to underestimate the degree of discrimination.