While most RT experiments yield a single point on the speed-accuracy tradeoff — a mean RT paired with an accuracy level — the SAT function methodology traces out the entire time course of information processing. By systematically varying the time at which a response is required, researchers can observe accuracy rising from chance to asymptote, producing a curve whose parameters quantify distinct aspects of cognitive processing.
The Exponential Approach to a Limit
The standard parametric form for the SATF, proposed by Wickelgren (1977) and elaborated by Dosher (1979), is an exponential approach to a limit:
d'(t) = 0, for t ≤ δ
λ = asymptotic accuracy (discriminability at unlimited time)
β = rate parameter (speed of information accrual)
δ = intercept (onset of above-chance accuracy)
Each parameter captures a distinct aspect of processing. The asymptote λ reflects the total amount of information available — it distinguishes conditions that differ in the quality or quantity of available evidence. The rate β reflects the speed of information accrual — faster rates mean information becomes available more quickly. The intercept δ reflects the time at which processing begins to produce usable information — it captures encoding time and any initial overhead.
Deriving the Full SAT Curve
The response-signal method is the primary technique for mapping SATFs. On each trial, a tone or visual cue signals the participant to respond immediately, and the lag between stimulus onset and the response signal is varied across trials (typically from ~100 ms to ~3000 ms). At short lags, accuracy is near chance because processing is interrupted early; at long lags, accuracy approaches asymptote. Fitting the three-parameter exponential to the resulting data yields the SATF.
The critical advantage of the SATF approach is that it separates speed and accuracy effects that are confounded in standard RT measures. Two conditions might produce the same mean RT but differ in the rate of information accrual (same intercept and asymptote, different β). Or they might reach different asymptotes but at the same rate. These dissociations are invisible in standard analyses but emerge clearly in the SATF framework.
Applications
SATFs have been applied extensively in memory research, where they distinguish between familiarity (fast-rising, lower asymptote) and recollection (slow-rising, higher asymptote) processes in recognition memory (Dosher, 1984; McElree, 2006). In sentence processing, SATFs have shown that syntactic garden-path sentences reduce the rate of information accrual without affecting asymptotic comprehension. In visual search, SATFs distinguish efficient (parallel) from inefficient (serial) search by their rate parameters.
The SATF methodology provides one of the most complete pictures of information processing dynamics available, complementing RT distribution analyses and sequential sampling models with a direct measurement of how discriminability evolves over time.