We review and demonstrate how an empirical Bayes method, shrinking a protein's sample variance towards a pooled estimate, leads to far more powerful and stable inference to detect significant changes in protein abundance compared to ordinary t-tests. Using examples from isobaric mass labelled proteomic experiments we show how to analyze data from multiple experiments simultaneously, and discuss the effects of missing data on the inference. We also present easy to use open source software for normalization of mass spectrometry data and inference based on moderated test statistics.