Adaptive staircases — when and how

If you want to know the smallest colour difference a person can detect, or the quietest tone, or the briefest mask duration, you need a staircase. Fixed stimulus levels waste trials on levels nowhere near threshold and give you a threshold estimate only as fine-grained as your step size.

The minimal staircase

The simplest useful design is 1-up-2-down: after a correct response, you move toward the harder direction; after two incorrect responses, you move back toward easier. This rule converges on the stimulus level where the participant is correct ~71% of the time — a defensible psychometric threshold.

Common tweaks:

• Step size decrease. Start with large steps (log units), halve the step after each reversal. Early reversals are throwaway; later ones are your measurement.
• Stopping rule. Stop after N reversals (typically 6 or 8), average the last M reversals (typically 4) as the threshold estimate.
• Interleaved staircases. Run 2+ independent staircases in random order to prevent prediction-based strategies.

When a staircase is the wrong tool

• Your DV is a preference, not an accuracy — use ranking.
• You need the full psychometric function, not just threshold — use method of constant stimuli.
• Your stimulus manipulation isn't monotonic — staircases assume harder → lower accuracy; a staircase across semantically unrelated conditions is nonsense.

References

• Levitt, H. (1971). Transformed up-down methods in psychoacoustics. Journal of the Acoustical Society of America, 49(2B), 467–477.
• Cornsweet, T. N. (1962). The staircase-method in psychophysics. American Journal of Psychology, 75(3), 485–491.
• Kingdom, F. A. A., & Prins, N. (2016). Psychophysics: A Practical Introduction (2nd ed.). Academic Press.