In 1966, Saul Sternberg introduced an elegantly simple paradigm that has become one of the most influential experimental designs in cognitive psychology. Participants memorize a small set of items (the "memory set," typically 1–6 digits), then see a single probe item and must rapidly indicate whether the probe was in the memory set. The fundamental finding — that RT increases linearly with memory set size — has profound implications for the nature of memory retrieval.
The Linear RT Function
a ≈ 400 ms (intercept: encoding + response execution)
b ≈ 38 ms/item (slope: time per comparison)
n = number of items in memory set
The linearity of the RT-set size function is remarkably robust, holding across different stimulus types, modalities, and populations. The slope b — approximately 35–40 ms per item in the original studies — has been interpreted as the time required to compare the probe to one memory item. The intercept a captures stimulus encoding and response execution processes.
Serial Exhaustive Search
The most striking aspect of Sternberg's results is that the slope is the same for positive (yes) and negative (no) responses. If search terminated upon finding a match (serial self-terminating search), positive responses should have a slope of b/2 on average (finding the match on average halfway through the list), while negative responses should have a slope of b. Instead, equal slopes suggest serial exhaustive search — the entire memory set is scanned before a response is initiated, even when a match is found early.
The exhaustive search finding initially seemed paradoxical: why would the system continue searching after finding a match? Sternberg suggested that the comparison process is so fast that the overhead of checking for a match after each comparison would actually slow down the overall process. It is more efficient to scan all items quickly and make a single decision at the end than to check for a match after each comparison. This is analogous to the engineering tradeoff between simple, fast processors and complex, slower ones.
Alternative Models
The serial exhaustive interpretation has been challenged by parallel processing models. Townsend and colleagues demonstrated that unlimited-capacity parallel processing with a specific noise distribution can produce linear RT functions identical to those predicted by serial search (Townsend & Ashby, 1983). In such models, all memory items are compared simultaneously, but the time to complete all comparisons increases linearly with set size because the maximum of n independent comparison times grows approximately linearly for small n.
Direct-access models propose that probes directly activate their memory representations (if present) without serial comparison. The set-size effect in these models arises from increased interference or noise as more items are held in memory. McElree and Dosher (1989) used the response signal method to show that set-size effects in this paradigm affect primarily the asymptote of the SAT function, not the rate — a pattern more consistent with interference than with serial search.
Legacy
Regardless of the correct interpretation of the underlying mechanism, Sternberg's paradigm remains a benchmark task in cognitive psychology. It introduced the powerful logic that the form of the RT function (its slope, intercept, and linearity) constrains theories of cognitive architecture, anticipating the more general additive factors method that Sternberg would develop shortly afterward.