Predictions about the health risks of low level radiation combine two sorts of measures. One estimates the amount and kinds of radiation released into the environment, and the other estimates the adverse health effects. A new field called health physics integrates and applies nuclear physics to cytology to supply both these estimates. It does so by first determining the kinds of effects different types of radiation produce in biological organisms, and second, by monitoring the extent of these effects produced by given levels of exposure. This essay examines the interplay between evidential constraints and external, contextual interests and values in studying the biological hazards of radiation. By analyzing the debate over linear vs. quadratic dose response models, the essay focuses on problems of developing quantitative, rather than qualitative, estimates of the risks of increased cancer incidence in an exposed population.