Differential abundance analysis is controversial throughout microbiome research. Gold standard approaches require laborious measurements of total microbial load, or absolute number of microorganisms, to accurately determine taxonomic shifts. Therefore, most studies rely on relative abundance data. Here, we demonstrate common pitfalls in comparing relative abundance across samples and identify two solutions that reveal microbial changes without the need to estimate total microbial load. We define the notion of "reference frames", which provide deep intuition about the compositional nature of microbiome data. In an oral time series experiment, reference frames alleviate false positives and produce consistent results on both raw and cell-count normalized data. Furthermore, reference frames identify consistent, differentially abundant microbes previously undetected in two independent published datasets from subjects with atopic dermatitis. These methods allow reassessment of published relative abundance data to reveal reproducible microbial changes from standard sequencing output without the need for new assays.