Scientists are divided on the status of hypothesis H that low doses of ionizing radiation (under 20 rads) cause hormetic (or non-harmful) effects. Military and industrial scientists tend to accept H, while medical and environmental scientists tend to reject it. Proponents of the strong programme claim this debate shows that uncertain science can be clarified only by greater attention to the social values influencing it. While they are in part correct, this paper argues that methodological analyses (not merely attention to social values) also can help clarify uncertain science. The paper analyzes five measurement uncertainties, as well as seven methodological value judgments, relevant to H. Using criteria of internal and external consistency, as well as predictive power, it argues that metascience also helps resolve this debate. And if so, then value-laden, policy-relevant science may need, not only more attention to social values in order to resolve and to clarify disputes, but also more conceptual and methodological analyses of science. (This paper suggests what such methodological analyses might be like and uses the case of low-dose risks from radiation to illustrate its points, while a companion paper ("Chemical Hormesis, Conceptual Clarification, and the Warrant for Policy-Driven Science") in this same issue of POS suggests what such conceptual analyses might be like and uses the case of low-dose risks from chemicals to illustrate its points.) If this paper's thesis holds in the very politicized "hard case" of radiation hormesis, then it suggests that the metascientists may be right about what is also often necessary to clarify scientific disputes.