Many people know about the National Center for Education Statistics (NCES) and the Bureau of Labor Statistics (BLS), but have you heard of the National Center for Science and Engineering Statistics (NCSES)? NCSES was established within the National Science Foundation in 2010 and is "the nation's leading provider of statistical data on the U.S. science and engineering enterprise:"
their site you can find information about "research and development,
the science and engineering workforce, the condition and progress of
STEM education, and U.S. competitiveness in science, engineering,
technology, and R&D." If you want to do a scientific study of
science or scientists, this would be the place to start.