Error-controlled lossy compressors have been widely used in scientific applications to reduce the unprecedented size of scientific data while keeping data distortion within a user-specified threshold. While they significantly mitigate the pressure for data storage and transmission, they prolong the time to access the data because decompression is required to transform the binary compressed data into meaningful floating-point numbers. This incurs noticeable overhead for common analytical operations on scientific data that extract or derive useful information, because the time cost of the operations could be much lower than that of decompression. In this work, we design an error-controlled lossy compression and analytical framework that features multi-stage decompression and homomorphic analytical operation algorithms on intermediate decompressed data for reduced data access latency. Our contributions are threefold. (1) We abstract a generic compression pipeline with partial decompression to multiple intermediate data representations and implement four instances based on state-of-the-art high-throughput scientific data compressors. (2) We carefully design homomorphic algorithms to enable direct operations on intermediate decompressed data for three types of analytical operations on scientific data. (3) We evaluate our approach using five real-world scientific datasets. Experimental evaluations demonstrate that our method achieves significant speedups when performing analytical operations on compressed scientific data across all three targeted analytical operation types.