The speed-accuracy trade-off (SAT) suggests that time constraints reduce response accuracy. Its relevance in observational settings--where response time (RT) may not be constrained but respondent speed may still vary--is unclear. Using 29 data sets containing data from cognitive tasks, we use a flexible method for identification of the SAT (which we test in extensive simulation studies) to probe whether the SAT holds. We find inconsistent relationships between time and accuracy; marginal increases in time use for an individual do not necessarily predict increases in accuracy. Additionally, the speed-accuracy relationship may depend on the underlying difficulty of the interaction. We also consider the analysis of items and individuals; of particular interest is the observation that respondents who exhibit more within-person variation in response speed are typically of lower ability. We further find that RT is typically a weak predictor of response accuracy. Our findings document a range of empirical phenomena that should inform future modeling of RTs collected in observational settings. [This work was co-written by the Project iLEAD Consortium.]