Introduction:

Weber-Fechner's law is an impressive example of early attempts to study the human response to a physical stimulus in a quantitative fashion. We attempted to develop an experiment avoiding the pitfalls of adaptational responses and suitable for training undergraduate students in data analysis using standard software.

Methods:

132 undergraduate students working in groups of 2 were given a non-toxic red stock solution (e.g. cherry juice, 100%) and water (0%) and asked to prepare samples of 50%, 25%, 12.5%, 6.25% and 3.125% concentration (“x”) via serial dilution. The two students in the group and one uninvolved test person then ranked the staining intensity of the solutions on a subjective linear scale (“?(x)”) ranging from 10 (pure stock solution, bright red) to 0 (pure water). The concentrations “x” of the solutions and the subjective estimates of staining intensity “?(x)” were entered into a pre-prepared excel worksheet. Instructions were given on how to calculate the mean (n=3), plot the results, and fit the data with a logarithmic function.

Results:

In all but one of the 66 groups, a logarithmic fit of ?(x) versus x yielded a coefficient of determiniation R² > 0.90, in 58 groups, R² was > 0.97. A fit of the means of all 132 measurements gave ?(x) = 2.5·Ln(x) - 1.77 (R² = 0.99).

Conclusions:

Subjective estimates of staining intensity closely follow Weber-Fechner's law. A model based on the Goldman-Hodgkin-Katz equation is developed on a separate spreadsheet; the limits of the model are discussed.