Researchers usually discretize a continuous dependent variable into two target classes by introducing an artificial discretization threshold (e.g., median). However, such discretization may introduce noise (i.e., discretization noise) due to ambiguous class loyalty of data points that are close to the artificial threshold. Previous studies do not provide a clear directive on the impact of discretization noise on the classifiers and how to handle such noise. In this paper, we propose a framework to help researchers and practitioners systematically estimate the impact of discretization noise on classifiers in terms of its impact on various performance measures and the interpretation of classifiers. Through a case study of seven software engineering datasets, we find that: 1) discretization noise affects the different performance measures of a classifier differently for different datasets; 2) Though the interpretation of the classifiers are impacted by the discretization noise on the whole, the top 3 most important features are not affected by the discretization noise. Therefore, we suggest that practitioners and researchers use our framework to understand the impact of discretization noise on the performance of their built classifiers and estimate the exact amount of discretization noise to be discarded from the dataset to avoid the negative impact of such noise.