Cells from the same individual share a common genetic and environmental background and are not independent, therefore they are subsamples or pseudoreplicates. Thus, single-cell data have a hierarchical structure that many current single-cell methods do not address, leading to biased inference, highly inflated type 1 error rates, and reduced robustness and reproducibility. This includes methods that use a batch effect correction for individual as a means of accounting for within sample correlation. Here, we document this dependence across a range of cell types and show that "pseudo-bulk" aggregation methods are overly conservative and underpowered relative to mixed models. We propose applying two-part hurdle generalized linear mixed models with a random effect for individual to properly account for both zero inflation and the correlation structure among measures from cells within an individual. Finally, we provide power estimates across a range of experimental conditions to assist researchers in designing appropriately powered studies. ### Competing Interest Statement The authors have declared no competing interest.

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