The speed-accuracy tradeoff: history, physiology, methodology, and behavior

Abstract

There are few behavioral effects as ubiquitous as the speed-accuracy tradeoff (SAT). From insects to rodents to primates, the tendency for decision speed to covary with decision accuracy seems an inescapable property of choice behavior. Recently, the SAT has received renewed interest, as neuroscience approaches begin to uncover its neural underpinnings and computational models are compelled to incorporate it as a necessary benchmark. The present work provides a comprehensive overview of SAT. First, I trace its history as a tractable behavioral phenomenon and the role it has played in shaping mathematical descriptions of the decision process. Second, I present a "users guide" of SAT methodology, including a critical review of common experimental manipulations and analysis techniques and a treatment of the typical behavioral patterns that emerge when SAT is manipulated directly. Finally, I review applications of this methodology in several domains.

Keywords: decision-making; speed-accuracy tradeoff.

Figure 1

Random-walk model of choice reaction time. (A) Each sample can be considered evidence favoring one of two options, and at each step, the observer updates an estimate of the posterior probability (here, presented as an odds ratio) based on that evidence. A response is produced at a threshold odds ratio. Reaction time is not explicit, but proportional to the total number of samples. Adapted from Fitts (1966). (B) The closely related diffusion model. Here, boundaries are associated with the correct or errant response and the X-axis is real-time. As in (A) responses are produced when activation reaches threshold, and the SAT is a function of the placement of the threshold. Adapted from Ratcliff and Rouder (1998).

Figure 2

Data from Heitz and Engle (2007) Experiments 1 and 2. (A) Data were fit by an exponential approach to a limit. The critical pattern concerns the incompatible condition (dashed lines). The groups do not differ in intercept or in asymptote, but do differ in rate. (B) The same data in (A) linearized using a log-odds transformation and fit with a log-linear regression.

Figure 3

Comparison of the SATF, overall CAF, and individual CAFs in the same simulated dataset. (A) The SATF is simply the mean RT and accuracy rate for each SAT condition Here, they were 225, 325, and 425 ms response deadlines. The manipulation was effective by definition, yielding accuracy rates of 50, 70, and 90%, respectively. Each condition was constructed by drawing N = 10,000 observations randomly from an ex-Gaussian distribution with parameters indicated in figure inset. Solid histograms depict correct trials, open histograms error trials. (B) The same data as (A) but aggregated disregarding SAT condition and plotted as a CAF. (C) Same data as (A,B) but CAFs computed separately for each deadline condition.

Figure 4

Two empirical examples when the CAF—both the overall CAF and individual CAFs overlap with the SATF. (A) (Schouten and Bekker, 1967) forced subjects to respond to respond at target RTs during a simple two-choice response time experiment. They found that the individual CAFs overlapped significantly; the accuracy rate associated with a given RT was invariant with respect to the forced response time condition. The overall CAF and SATF are approximated by the black ogive running through individual points. Data were traced using graphics software from the original work. Note that error rate (rather than accuracy rate) is plotted on the y-axis. (B) (Heitz and Engle, 2007) presented subjects with a two choice response compatibility experiment under 6 response deadlines. These data, replotted from their incompatible condition, clearly indicate gross agreement between the SATF (black), overall CAF (red), and individual CAFs (colored lines). Based on this agreement, these authors used the overall CAF as their primary measure to retain time resolution.

Figure 5

Dependence of the CAF on component RT variance and direction of mean vs. correct RT. (A–C) With small RT variability, distributions exhibit little overlap, leading the overall CAF (red lines) to be a fair representation of the SATF with better resolution in time. The form of the individual CAFs (blue) are dictated by the direction of correct and error RT, exhibiting a downward trend for slow errors (A) a flat line with equal mean correct and error RT (B) and an upward trend for fast errors (C). (D–F) The mismatch between SATF, overall CAF, and individual CAFs is exaggerated with more reasonable parameters. When RT distributions significantly overlap, the overall CAF no longer reflects the SATF.

Figure 6

Quantile-probability plots. (A) The QPP calculated from a single non-human primate during an SAT task. Open points to the left of 0.5 correspond to errors, closed points to the right of 0.5 are correct trials. Each vertically oriented set of 5 points mark the RT quantiles described in the text. Lines connect quantiles between SAT conditions (red = Accuracy stress, black = Neutral, and green = Speed stress). (B) The QPP calculated from the same simulated dataset presented in Figure 3. The individual-condition RT distributions (Figure 3C) are reflected in the quantiles of the QPP.