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This paper makes a contribution towards the statistical analysis of data sets containing intervals, that naturally arises in survey contexts. The suggested approach is sufficiently general to cover most cases where interval data are used. Interval data appear in many contexts, such as in reliability studies and survival analysis, in medicine and economics, in opinion elicit surveys, etc. There are several reasons for the extensive use of interval data, perhaps, the most common being one of necessity; exact values of the underlying observations are censored. The nature of the intervals analyzed here is somewhat unusual. The self-selected intervals (SeSeI) are (freely) chosen by the subjects. A generalization of the influential approach has been suggested to the statistical analysis of general censoring introduced by B. W. Turnbull. A key independence assumption in Turnbull's analysis has been explained and generalized. A sampling stopping rule based on the coverage probability has been suggested and the properties of a two-step estimator, based on the idea of asking two questions, where the second involves a way of fine-graining the information, has been discussed. This paper provides several informatics methods for SeSeI, targeting the problem of partial nonparametric identification. The properties of the suggested statistical models are stated, including a recursion for easy numerical calculations. An extensive simulation study, displaying, inter alia, the usefulness of the proposed resampling methods for the situation under study, completes the paper.