The power of human induced pluripotent stem cell (hiPSC)-based studies to resolve the smaller effects of common variants within the size of cohorts that can be realistically assembled remains uncertain. We identified and accounted for a variety of technical and biological sources of variation in a large case/control schizophrenia (SZ) hiPSC-derived cohort of neural progenitor cells and neurons. Reducing the stochastic effects of the differentiation process by correcting for cell type composition boosted the SZ signal and increased the concordance with post-mortem data sets. We predict a growing convergence between hiPSC and post-mortem studies as both approaches expand to larger cohort sizes. For studies of complex genetic disorders, to maximize the power of hiPSC cohorts currently feasible, in most cases and whenever possible, we recommend expanding the number of individuals even at the expense of the number of replicate hiPSC clones.