Magnitude estimation asks observers to assign numbers to stimuli such that the numbers reflect the perceived magnitude of the attribute. If a sound seems twice as loud as a reference, the observer assigns a number twice as large. This direct scaling method, pioneered by S. S. Stevens in the 1950s, bypasses the indirect inference from JNDs used by Fechner and produces data that consistently follow Stevens' Power Law.
Procedure
In a typical experiment, a reference stimulus (the modulus) is assigned a fixed number, and subsequent stimuli are judged relative to it. Alternatively, in free modulus designs, observers choose their own reference number. Data are typically analyzed by computing geometric means of judgments at each stimulus level and fitting a power function in log-log coordinates, where the slope gives the exponent directly.
Slope n = exponent (modality-specific)
Intercept log k = scale constant
Cross-Modality Matching
Stevens also developed cross-modality matching, where observers adjust a stimulus on one continuum to match the perceived intensity of a stimulus on another. If both modalities follow power laws with exponents n₁ and n₂, the matching function should be a power function with exponent n₁/n₂. This prediction has been confirmed across many modality pairs, providing strong evidence for the power law framework.
Magnitude estimation has been criticized for response biases: observers tend to avoid extreme numbers, compress their response range, and anchor on previous responses. These biases can distort the estimated exponent. Alternatives such as magnitude production (adjusting stimulus to match a given number) and functional measurement (Anderson's information integration theory) address some of these concerns.