Reaction Time & Hick's Law Lab

Try It Yourself

Choices N (Hick's Law)

Pick N, click "Start Live Trial", wait for the lit dot, then click that same dot as fast as you can.

Simulated Subject (auto-run)

Trials per batch 300

Response noise σ (ms) 35

Least-Squares Fit (simulated trials)

Trials run

R²

–

Fitted a (ms)

–

Fitted b (ms/bit)

–

True a / b

180 / 150

Recovery error

–

How it works

Hick's Law (Hick 1952, Hyman 1953): choice reaction time grows logarithmically with the number of equally-likely options N, because each doubling of N adds exactly one more bit of information the nervous system must resolve before it can respond:

RT(N) = a + b · log2(N)

a ≈ 180 ms is the irreducible sensorimotor floor (stimulus transduction, nerve conduction, muscle activation — present even at N=1, "simple reaction time"). b ≈ 150 ms/bit is the information-processing rate.

Try It Yourself runs the real classic choice-RT apparatus: N positions are shown, one lights up at a random, unpredictable moment, and your own click-to-light latency is timestamped with performance.now() and plotted as a white diamond. Clicking the wrong lit position counts as an error and is discarded, like a real psychophysics protocol.

Simulated Subject draws trials from RT = a + b·log2(N) + Normal(0, σ) with N resampled uniformly from {1,2,4,8} each trial (fixed a=180, b=150 — the values printed under "True a / b"), plotted as orange dots. A least-squares line is fitted from scratch to the accumulated (log2 N, RT) pairs:

slope b̂  = Σ(x-x̄)(y-ȳ) / Σ(x-x̄)²
intercept â = ȳ - b̂·x̄

Run a few hundred trials and watch the fitted â/b̂ converge onto the true 180/150 that generated the noise — numerical proof that Hick's logarithmic relationship is both present in, and recoverable from, noisy single-trial data.

Choice task — N=2

RT vs log2(N) — live regression