The partial pressure of CO₂ in the oceans has increased rapidly over the past century, driving ocean acidification and raising concern for the stability of marine ecosystems^1,2,3. Coral reef fishes are predicted to be especially susceptible to end-of-century ocean acidification on the basis of several high-profile papers^4,5 that have reported profound behavioural and sensory impairments—for example, complete attraction to the chemical cues of predators under conditions of ocean acidification. Here, we comprehensively and transparently show that—in contrast to previous studies—end-of-century ocean acidification levels have negligible effects on important behaviours of coral reef fishes, such as the avoidance of chemical cues from predators, fish activity levels and behavioural lateralization (left–right turning preference). Using data simulations, we additionally show that the large effect sizes and small within-group variances that have been reported in several previous studies are highly improbable. Together, our findings indicate that the reported effects of ocean acidification on the behaviour of coral reef fishes are not reproducible, suggesting that behavioural perturbations will not be a major consequence for coral reef fishes in high CO₂ oceans. The full (paywalled) article appeared on the Nature website at https://www.nature.com/articles/s41586-019-1903-y