Theory testing, statistical methodology, and the growth of experimental knowledge

The idea that scientific progress is a matter of the growth of experimental knowledge has several implications for an adequate methodology of evidence, inference, and testing. Far from desiring an account for rationally accepting, preferring, or "probabilifying" large-scale theories with limited evidence, we need an account that shows us how to learn more about the phenomena of interest by probing individual hypotheses severely. I illustrate with experimental general relativity from 1960-1980. Progress hinged on systematically considering how discrepancies in key parameters could have failed to be detected with existing data. An understanding of statistical methodology shows how we learn about theoretical parameters and hypotheses by means of experimental parameters and hypotheses that are identical, or are good approximations, to the theoretical ones.