The human microbiome, or the set of bacteria that live in and on a person, have been shown in the past decade to be associated with many facets of human health, including metabolism, immune function, and cognition. Longitudinal studies of the microbiome are becoming increasingly common as a way to investigate within- and between-subject variability in microbial profiles. The amount of instability, or volatility, in the microbial community has been associated with conditions such as irritable bowel disease, stress, and antibiotic treatment. However, there is no clear framework for quantifying the extent of volatility in the microbiome to enable association testing with outcomes of interest. We propose formal measures of qualitative (appearance or disappearance) and quantitative (abundance) volatility, explore patterns of volatility in real longitudinal microbiome datasets, propose a hypothesis testing framework, and assess performance across a range of study designs and simulation settings. We apply the approach to investigate microbiome volatility across irritable bowel syndrome subtypes.