We conduct an experiment to (i) measure the structure of preferences over lotteries and (ii) test for stability of the probability transformation functions over different choice sets. The design is based on manipulations of the 'probability triangle' A disaggregated nonparametric analysis in which we classify subjects according to which transformation function is most consistent with their revealed choice behavior shows that a linear and a strictly concave transformation function are the most common for risky choice. We find essentially no evidence of an S-shaped transformation function for choice under risk. Formal econometric estimation clearly rejects the S-shaped function in favor a strictly concave function. The difference between our results and those of previous studies can be attributed to the choice of functional forms used in estimating the transformation function, to the limited space of lotteries upon which estimates have been based, and to the certainty-equivalent method used to elicit responses in those studies.