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Advances in protein tagging and mass spectrometry have enabled generation of large quantitative proteome and phosphoproteome data sets, for identifying differentially expressed targets in case-control studies. The power study of statistical tests is critical for designing strategies for effective target identification and control of experimental cost. Here, we develop a simulation framework to generate realistic phospho-peptide data with known changes between cases and controls. Using this framework, we quantify the performance of traditional -tests, Bayesian tests, and the ranking-by-fold-change test. Bayesian tests, which share variance information among peptides, outperform the traditional -tests. Although ranking-by-fold-change has similar power as the Bayesian tests, its type I error rate cannot be properly controlled without proper permutation analysis; therefore, simply relying on the ranking likely brings false positives. Two-sample Bayesian tests considering dependencies between intensity and variance are superior for data sets with complex variance. While increasing the sample size enhances the statistical tests' performance, balanced controls and cases are recommended over a one-side weighted group. Further, higher peptide standard deviations require higher fold changes to achieve the same statistical power. Together, these results highlight the importance of model-informed experimental design and principled statistical analyses when working with large-scale proteomics and phosphoproteomics data.