Sensitivity data is defined as involving two response categories, with responses observed at different levels of some variable. The responses are taken to indicate sensitivity to the variable and may be labeled "positive" or "negative." The countback method offers confidence limits for the 50% point, the level of the variable for which the two responses are equally likely, in the special case when only one response is observed at each level. A lower bound on the confidence coefficient for these limits can be given, assuming only independent responses and the existence of something like a 50% point. No specific model of response probabilities is required, and the variable need not even be continuous. To gain a greater understanding of the countback method, it is used here to analyze sensitivity data obtained in an experiment on the perception of depth in pictures, and to study two artificial situations where the response probabilities can be specified exactly. The countback method is compared with the minimum Chi-square and the maximum likelihood estimation methods and its extension to data with more than one response per level is discussed. The results suggest that the countback method has a significant place among previous methods for analyzing sensitivity data. Appendices include historical, statistical, simulation, and experimental details. (Author/CK)