Is it legal for employers to reveal personality test data publicly?

Can an employer require employees to publicly reveal their Myers-Briggs (MBTI) and LOC personality test results to all fellow co-workers in a required staff workshop? Would psychological data be considered confidential and not legally open to public scrutiny, even that of the common rank and file coworkers? In a few weeks, my entire local government department is required to take a staff in-service training day. One of the activities is taking our MBTI and LOC scores, naming each person's results in front of all staff, discussing it, and doing other activities related to the psychology test results. What are our legal rights as employees concerning this? I know employers can make employees take these type tests but I was not aware that they could broadcast the test results in a indiscriminate public manner. What federal/state statutes cover this? Any help on this would be appreciated. Thanks!