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Single-cell CRISPR screens such as Perturb-seq enable transcriptomic profiling of genetic perturbations at scale. However, the data produced by these screens are noisy, and many effects may go undetected. Here we introduce transcriptome-wide analysis of differential expression (TRADE)-a statistical model for the distribution of true differential expression effects that accounts for estimation error appropriately. TRADE estimates the 'transcriptome-wide impact', which quantifies the total effect of a perturbation across the transcriptome. Analyzing several large Perturb-seq datasets, we show that many transcriptional effects remain undetected in standard analyses but emerge in aggregate using TRADE. A typical gene perturbation affects an estimated 45 genes, whereas a typical essential gene affects over 500. We find moderate consistency of perturbation effects across cell types, identify perturbations where transcriptional responses vary qualitatively across dosage levels and clarify the relationship between genetic and transcriptomic correlations across neuropsychiatric disorders.