How many (distinguishable) classes can we identify in single-particle analysis?

Heterogeneity in cryoEM is essential for capturing the structural variability of macromolecules, reflecting their functional states and biological significance. However, estimating heterogeneity remains challenging due to particle misclassification and algorithmic biases, which can lead to reconstructions that blend distinct conformations or fail to resolve subtle differences. Furthermore, the low signal-to-noise ratio inherent in cryo-EM data makes it nearly impossible to detect minute structural changes, as noise often obscures subtle variations in macromolecular projections. In this paper, we investigate the use of p-values associated with the null hypothesis that the observed classification differs from a random partition of the input data set, thereby providing a statistical framework for determining the number of distinguishable classes present in a given data set.