The only difference would be some of the electives and general education requirements. BA degrees usually have a foreign language requirement.
You probably would have to take more math, sciences, and computer classes (and less language and social science classes) with a BS. When I was looking at BA/BS programs, I noticed social science programs that had a BS made students take more statistics classes and more biology/chemistry classes. They also had to take neuro-psychology and study the brain/brain chemcials in depth. However, these classes will help better prepare you for graduate school. If you want to take the Social Psychology route, then a BA would be fine... otherwise, go for the BS.
Generally, BA degrees require a specific amount of foreign language classes in order to graduate. In contrast, you usually have to take more reasoning classes ( i.e. math or philosophy) to graduate with a BS.
It depends on the institution and the psychology department within the school as to which focus they prefer.
The BA has a broader scope, with a strong emphasis on the humanities, theoretical and general knowledge in a recognized discipline, interdisciplinary field, or of a professional study.
The BS is more of a focused approach with a science base to include a balance of liberal arts, technological knowledge, math and computer oriented skills, and practical skills needed for a particular discipline within the field
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