In tests of cognitive and physical performance, the trade-off between speed and accuracy requires that the two be studied together. A natural question is whether speed-accuracy coupling depends on other variables, such as sustained attention. We propose CoCoA (Conditional Correlation Model with Association Size), a likelihood-based statistical framework to estimate the conditional correlation between speed and accuracy as a function of additional variables. We also propose novel measures of the association size, which are analogous to effect sizes on the correlation scale, while adjusting for confounding. In simulation studies, we identify and compare likelihood-based estimators of conditional correlation to semi-parametric estimators adapted from genome association studies, and find that the former fare better under both ideal settings and misspecification. Using neurocognitive data from the Philadelphia Neurodevelopmental Cohort, we demonstrate that greater sustained attention is associated with stronger speed-accuracy coupling in a complex reasoning task while controlling for age.