Traditional analyses of reaction time compare condition means, implicitly assuming that experimental effects are constant across the entire RT distribution. Delta plots challenge this assumption by examining how the magnitude of an effect varies from fast to slow responses. This distributional perspective has revealed qualitatively different patterns across tasks and has become a key tool for distinguishing between competing cognitive models.
Construction
Delta plots are constructed as follows: (1) for each condition, compute Vincentized quantiles (e.g., at the .1, .3, .5, .7, .9 quantile fractions); (2) for each quantile, compute the RT difference between conditions (the delta); (3) plot each delta against the average RT at that quantile. The resulting function Δ(RT) shows how the experimental effect grows, shrinks, or reverses across the speed of responding.
Δ(p) = Q_B(p) − Q_A(p)
Average(p) = [Q_A(p) + Q_B(p)] / 2
Plot: Δ(p) vs. Average(p)
Common Patterns
Three canonical delta plot shapes have been identified:
Positive slope: The effect increases with RT. This is the most common pattern and is consistent with effects that influence the rate of evidence accumulation (drift rate in diffusion models). Slower responses are more affected because there is more time for the manipulation to exert its influence.
Flat (zero slope): The effect is constant across the distribution. This pattern suggests a pure shift of the distribution, consistent with effects on non-decision time (e.g., stimulus encoding or motor execution differences).
Negative slope: The effect decreases with RT — fast responses show a larger effect than slow responses. This distinctive pattern is observed in the Simon effect and Eriksen flanker task for the incompatible condition, and is thought to reflect the suppression of an initial automatic activation over time.
The Simon effect shows a striking negative-going delta plot: the fastest responses show a large compatibility effect, but the slowest responses show a reduced or even reversed effect. This pattern has been interpreted as evidence for the dual-route model, in which an automatic spatial activation (that creates the Simon effect) is actively suppressed over time by a controlled process, so that slow responses have had more time to overcome the automatic interference.
Theoretical Implications
Delta plots have become diagnostic tools for theory testing because different cognitive architectures predict different delta plot shapes. Drift rate effects in the diffusion model produce positive slopes; boundary separation effects produce near-zero slopes at the fast end with increasing effects at the slow end; non-decision time effects produce flat delta plots. This makes delta plots a valuable complement to mean RT and accuracy analyses, providing distributional constraints that theoretical models must satisfy.
Schwarz and Miller (2012) provided a formal mathematical analysis showing that delta plot slopes can be derived analytically from the parametric forms of the underlying RT distributions, linking the empirical patterns to specific model parameters.