Statistical & Clinical Analysis
Hick-Hyman Law Formula: Choice Reaction Time RT = a + b * log2(n + 1)
Quantify menu-navigation and cockpit decision latency across n equally probable choices using William Edmund Hick (1952) and Ray Hyman’s (1953) logarithmic law RT = a + b * LOG(n + 1, 2).
Why doubling menu items adds a CONSTANT ~150 ms decision step instead of doubling reaction time!
William Edmund Hick (1952, Quarterly Journal of Experimental Psychology) and Ray Hyman (1953, Journal of Experimental Psychology) demonstrated that human choice reaction time scales linearly with Shannon information entropy H (bits), not raw option count n! For n equally probable stimulus-response alternatives—plus "+ 1" representing uncertainty about WHEN/WHETHER a stimulus occurs—effective transmitted information is H = LOG(n + 1, 2) bits, giving RT = a + b * LOG(n + 1, 2)!
With perceptual-motor baseline a = 0.18 s and cognitive binary-search slope b = 0.15 s/bit (~6.7 bits/s processing rate), choosing among n = 7 equally likely cockpit alerts or ungrouped menu options carries H = LOG(8, 2) = 3.0000 bits and RT = 0.18 + 0.15 * 3 = 0.6300 s (630 ms), whereas a simple 1-option trigger (n = 1 -> LOG(2, 2) = 1 bit) takes only 0.3300 s!
| Equally Probable Choices n | Hick Entropy LOG(n + 1, 2) | Choice Reaction Time RT (a=0.18s, b=0.15s/bit) |
|---|---|---|
| n = 1 Single Action | 1.0000 bit | 0.3300 seconds (330 ms) |
| n = 7 Ungrouped Menu Choices | 3.0000 bits | 0.6300 seconds (630 ms) |
| n = 15 Choices (+1 bit over n=7) | 4.0000 bits | 0.7800 seconds (+150 ms constant step) |
Hick-Hyman Choice Reaction Time RT (s) = a + b * LOG(n + 1, 2)
Computes expected decision reaction time in seconds for n >= 1 equally likely alternatives (B2), baseline latency a (B3, s), and entropy slope b (B4, s/bit).
=IF(OR(B2 < 1, B3 < 0, B4 <= 0), "Requires n >= 1 Choices & Positive Slope", ROUND(B3 + B4 * LOG(B2 + 1, 2), 4))Hick Stimulus Uncertainty Information Load H = LOG(n + 1, 2) (Bits)
Evaluates base-2 information load in bits including the +1 non-occurrence state.
=IF(OR(B2 < 1, B3 < 0, B4 <= 0), "Requires n >= 1 Choices & Positive Slope", ROUND(LOG(B2 + 1, 2), 4))Try the example
Use the original values or change them to test your understanding.