Statistically - while this study is from 2003, it demonstrates one methodology that could be used: Send out a bunch of resumes that are *identical*, except for the name at the top. Give some "white" names, and others names more likely associated with various racial minorities. See which ones get more callbacks.
http://www.nber.org/digest/sep03/w9873.html
You can do the same for traditionally male and female names:
"Moss-Racusin wanted to figure out if faculty at academic institutions, despite their training in conducting scientifically objective research, held implicit gender biases that were disadvantaging women who were pursuing STEM careers.
In their study, Moss-Racusin and her colleagues created a fictitious resume of an applicant for a lab manager position. Two versions of the resume were produced that varied in only one, very significant, detail: the name at the top. One applicant was named Jennifer and the other John. Moss-Racusin and her colleagues then asked STEM professors from across the country to assess the resume. Over one hundred biologists, chemists, and physicists at academic institutions agreed to do so. Each scientist was randomly assigned to review either Jennifer or John's resume.
The results were surprising—they show that the decision makers did not evaluate the resume purely on its merits. Despite having the exact same qualifications and experience as John, Jennifer was perceived as significantly less competent. As a result, Jenifer experienced a number of disadvantages that would have hindered her career advancement if she were a real applicant. Because they perceived the female candidate as less competent, the scientists in the study were less willing to mentor Jennifer or to hire her as a lab manager. They also recommended paying her a lower salary. Jennifer was offered, on average, $4,000 per year (13%) less than John."
http://gender.stanford.edu/news/2014/why-does-john-get-stem-job-rather-jennifer