In the two-alternative forced choice (2AFC) paradigm, two intervals (or locations) are presented on each trial — one containing the signal, the other containing noise — and the observer indicates which interval contains the signal. Because the correct answer is always one of the two intervals, 2AFC eliminates response bias and provides a criterion-free measure of sensitivity.
Relationship to Yes/No d′
PC = proportion correct
d′₂AFC = d′_yes/no × √2 (when equal-variance Gaussian)
Chance = 50% correct (d′ = 0)
The √2 factor arises because in 2AFC the observer effectively takes the difference between two independent samples (one from the signal distribution, one from the noise distribution), and this differencing operation increases sensitivity by √2 relative to a single observation. A 75% correct performance in 2AFC corresponds to d′ ≈ 0.95, while 90% correct gives d′ ≈ 1.81.
Advantages and Applications
The 2AFC paradigm is the workhorse of psychophysics because it eliminates criterion effects that can confound sensitivity measurement in yes/no tasks. It is the standard paradigm for measuring thresholds, fitting psychometric functions, and running adaptive procedures. Extensions include m-alternative forced choice (mAFC), where sensitivity is d′ = √2 × z(PC) only for m=2; for m>2, the relationship involves the maximum of m−1 independent normal samples.