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Formal concept analysis (FCA) and hierarchical classes analysis (HCA) can be viewed as two approaches of data analysis on data description and summarization, and focus on different characteristics of data in a formal context. In this paper, we propose a framework for classes analysis. The equivalence classes defined on object and attribute universes can be viewed as basic units of information in a formal context. The different data structures in FCA and HCA can be developed based on the equivalence classes. Furthermore, some basic sets of objects and attributes formed by equivalence classes can be used to compose other object and attribute sets, and they demonstrate connections between FCA and HCA. Through our studies, one can obtain an in-depth understanding of data analysis based on FCA and HCA.