Stevens:
Subjective scaling data collected by S. S. Stevens
Description
This experiment was apparently done by S. S. Stevens and colleagues in March 1962,
although the exact reference is lost. 10 subjects were played tones at each of
5 loudnesses, presumably in random order. Subjects were asked to
draw a line on paper whose length matched the loudness of the tone. Each
subject repeated each loudness 3 times, for a total of 30 trials per subject.
The original data are lost; reported here is the mean of the 3 log-lengths for
each loudness, the sd of the three log-lengths, and the number of replications,
which is always 3.
Format
A data frame with 50 observations on the following 5 variables.
subject- a factor with unique values for each subject
loudness- either 50, 60, 70, 80 or 90 db.
Decibels are a logrithmic scale
y- a numeric vector giving the mean of the log-lengths of
three lines drawn. Exponentiating these values would give the geometric mean
of the three lengths in cm.
sd- a numeric vector, giving the sd of the three log lengths
n- a numeric vector, equal to the constant value 3
Source
These data were obtained in the early 1970s from the data library in the
Harvard University Statistics Department.Details
This is a classic example of a psychophysics experiment pioneered by S. S.
Stevens. The basic idea is that the phychological response y to a physical
stimulus x should be proportional to x to a power. Since both the response
and the loudness are already in log-scale, linear fits should be expected.