A generalization of the bush-mosteller model with some significance tests

A generalization of the Bush-Mosteller learning model is proposed in connection with two-alternative learning situations with continuous reinforcement. The problem is to test the hypothesis that reward and non-reward are equally effective in promoting learning. Statistically this reduces to testing a hypothesis about the value of a single parameter, while a set of other parameters remains unspecified. The test presented has the property of being asymptotically locally most powerful among all tests of the same size and asymptotically similar. The application of the test is illustrated.I would like to express my gratitude to Professors J. Neyman and E. L. Scott, Department of Statistics, University of California, for their constant assistance and encouragement throughout the research that led to this paper and during its preparation, and to Professor F. W. Irwin, Department of Psychology, University of Pennsylvania, for his many helpful suggestions and comments.