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On the subject of personality tests, the Equal Employment Opportunity Commission (EEOC, see link below) states:
The use of tests and other selection procedures can be a very effective means of determining which applicants or employees are most qualified for a particular job. However, use of these tools can violate the federal anti-discrimination laws if an employer intentionally uses them to discriminate based on race, color, sex, national origin, religion, disability, or age (40 or older). Use of tests and other selection procedures can also violate the federal anti-discrimination laws if they disproportionately exclude people in a particular group by race, sex, or another covered basis, unless the employer can justify the test or procedure under the law.