This paper explores the use of binary segmentation procedures in two applications. The first application is concerned with the estimation of nonparametric quantal response curves. With Bernoulli data and an assumed monotone increasing curve, this gives rise a change-point model where the change points are determined using a sequence of nested hypothesis tests of whether a change point exists. The second application concerns cluster identification and inference for spatial data where the shape of the clusters and the number of clusters is unknown. The procedure involves a sequence of nested hypothesis tests of a single cluster versus a pair of distinct clusters. Examples of both applications are provided.