Data reduction procedures aim to minimize the impact of data acquisition imperfections on the measurement of data properties with a scientific meaning for the astronomer. To achieve this purpose, appropriate arithmetical manipulations with data and calibration frames must be performed. Furthermore, a full understanding of all the possible measurements relies on the firm constraint of their associated errors. We discuss different strategies for obtaining realistic determinations of final random errors. In particular, we highlight the benefits of considering the data reduction process as the full characterization of the raw data frames, but avoiding, as far as possible, the arithmetical manipulation of the data until the final measurement and analysis of the image properties. This approach will be used in the pipeline data reduction for ELMER and EMIR.