14 Paul Switzer

Press are collaborating with JSTOR to digitize, preserve and extend access to Biometrika. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. SUMMARY In the usual two-sample problem one is estimating the constant additive effect of a treatment or the additive constant by which two random variables differ. However, if the treatment-effect may depend on the response level, then a more general approach to two-sample problems seems appropriate. We define a treatment-effect function t and characterize distribution-free confidence bounds for the function t both in the case where t has specified parametric forms and in the case where t is not parameterized.