Real data example.

In genomic study, log transformation is a common prepossessing step to adjust for skewness in data. This standard approach often assumes that log-transformed data is normally distributed, and two sample t-test (or its modifications) is used for detecting differences between two experimental conditions. However, recently it was shown that two sample t-test can lead to exaggerated false positives, and the Wilcoxon-Mann-Whitney (WMW) test was proposed as an alternative for studies with larger sample sizes. In addition, studies have demonstrated that the specific distribution used in modeling genomic data has profound impact on the interpretation and validity of results. The aim of this paper is three-fold: 1) to present the Exp-gamma distribution (exponential-gamma distribution stands for log-transformed gamma distribution) as a proper biological and statistical model for the analysis of log-transformed protein abundance data from single-cell experiments; 2) to demonstrate the inappropriateness of two sample t-test and the WMW test in analyzing log-transformed protein abundance data; 3) to propose and evaluate statistical inference methods for hypothesis testing and confidence interval estimation when comparing two independent samples under the Exp-gamma distributions. The proposed methods are applied to analyze protein abundance data from a single-cell dataset.