An increasing number of studies are using single-cell RNA-sequencing (scRNA-seq) to characterize the gene expression profiles of individual cells. One common analysis applied to scRNA-seq data involves detecting differentially expressed (DE) genes between cells in different biological groups. However, many experiments are designed such that the cells to be compared are processed in separate plates or chips, meaning that the groupings are confounded with systematic plate effects. This confounding aspect is frequently ignored in DE analyses of scRNA-seq data. In this article, we demonstrate that failing to consider plate effects in the statistical model results in loss of type I error control. A solution is proposed whereby counts are summed from all cells in each plate and the count sums for all plates are used in the DE analysis. This restores type I error control in the presence of plate effects without compromising detection power in simulated data. Summation is also robust to varying numbers and library sizes of cells on each plate. Similar results are observed in DE analyses of real data where the use of count sums instead of single-cell counts improves specificity and the ranking of relevant genes. This suggests that summation can assist in maintaining statistical rigour in DE analyses of scRNA-seq data with plate effects.