Liquid chromatography-mass spectrometry-based (LC-MS) proteomics uses peak intensities of proteolytic peptides to infer the differential abundance of peptides/proteins. However, substantial run-to-run variability in intensities and observations (presence/absence) of peptides makes data analysis quite challenging. The missing observations in LC-MS proteomics data are difficult to address with traditional imputation-based approaches because the mechanisms by which data are missing are unknown a priori. Data can be missing due to random mechanisms such as experimental error or nonrandom mechanisms such as a true biological effect. We present a statistical approach that uses a test of independence known as a G-test to test the null hypothesis of independence between the number of missing values across experimental groups. We pair the G-test results, evaluating independence of missing data (IMD) with an analysis of variance (ANOVA) that uses only means and variances computed from the observed data. Each peptide is therefore represented by two statistical confidence metrics, one for qualitative differential observation and one for quantitative differential intensity. We use three LC-MS data sets to demonstrate the robustness and sensitivity of the IMD-ANOVA approach.