The psychological effect of a stimulus does not usually relate in a simple way to the physical strength of the stimulus. Besides suboptimal position of body and environmental interference, human sensory receptors do not respond linearly to physical stimulus, and the sensory system is also subject to internal noise. By controlling the presentation stimuli and the attention of the subject, and allowing for the effects of noise, a relation between the physical intensity and the perceived magnitude of the stimulus can be derived.
The first requirement in developing this relationship is to quantify perceptual experience. Scaling is an attempt to assign numbers to some property of a thing or group of things. Each of the following types of scales provides more information about the property being measured than those preceeding it.
nominal - numbers serve only to distinguish items from each other; there is no ordering of the resultant categories.
ordinal - numbers provide a rank ordering of items, though the differences between numbers do not reflect the amount of difference in the property.
interval - a certain numerical difference always reflects the same magnitude of difference in the property.
ratio - a number twice as large as another means that the property of one thing is double that of the other. (An interval scale with a true zero point.)
Most measurements in the social sciences are not ratio scales, because no absolute zero point is established.
The measurement of sensation began with Sanford's technique of category matching, where subjects were required to sort stimuli into several categories of equal perceptual "width". By judging each stimuli several times, (noise will cause instances of some stimuli to be judged into different categories) and averaging the category assignments for each stimulus, an ordinal scale is produced. Fechner developed "just noticable differences" as the units of an interval scale. Stevens developed a ratio scale using the log of the intensities of the stimuli and the perception.
A basic judgment in psychology is whether two stimuli are the same or different in some property. Given the uncertainty described by signal detection theory, a given difference will sometimes be judged different and sometimes judged the same. Therefore the threshold of detection (difference threshold) is defined probabalistically.
The following graphs show the results of a constant stimulus experiment for two subjects [purple and green curves; the purple curve shows a more sensitive observer]. Each subject is first presented with a standard stimulus, and then required to judge whether comparison stimuli, presented in random order, are larger than the standard. Each stimuli is presented multiple times, and the percentage of presentations where the subject responds "greater" is graphed against the objective value of the property being compared. [Usually "equal" is not a response option, because a "forced" guess shows greater sensitivity.]
The shapes of the curves show the subject's sensitivity. The light blue shading highlights the range of comparison values that the observer cannot reliably distinguish from the standard value. Because judging a comparison stimulus greater 50% of the time is equivalent to guessing, a subject who detects that there is a difference half of the time should answer "greater" on either 25% (for a smaller comparison) or 75% (for a larger comparison) of the trials for that stimulus. The average of the comparison magnitudes at these two percentages is called the point of subjective equality. [blue lines] (This method is more accurate than using the 50% response level.) The comparison stimulus difference between subjective equality and the detection (at least half of the time) of a difference from the standard (i.e., the 25% or 75% detection level) is called the (jnd) [horizontal arrows]. Using this method, Weber found that the jnd increased for more intense stimuli, at a constant rate. Thus:
jnd [change in intensity] = K * S [strength of initial stimulus]
K is a constant (known as the Weber fraction) whose value depends on the type of stimulus involved; typical values range from .013 for electric shock to .083 for sensitivity to the taste of salt.
Using Weber's fraction, and assuming that each jnd was perceptually equal to any other jnd, Fechner derived an equation (now called Fechner's law) that relates stimulus intensity and sensation magnitude:
S [sensation magnitude, in jnd's] = 1/K * log I [stimulus intensity]
This approximation is good under a wide range of conditions, but should be used as a guide rather than an exact relationship.
Stevens allowed subjects to directly assign values to the strength of a stimulus, producing the power law:
b Where S is the strength of sensation, k is a constant S = k I reflecting the design of the experiment, I is the stimulus intensity, and b is the exponent (constant for a given modality)
It is much easier to see the relationship if the Log base10 of both values is used; only the slope of a straight line must be fitted.
In indirect scaling, a standard stimulus is presented, and is defined to represent 1 unit of the property of interest. Each trial presents a comparison stimulus to the subject, who chooses a number which reflects the comparison's strength relative to the standard [i.e., 2 if the comparison is twice as strong, .1 for a tenth as strong, etc].
In direct scaling, or magnitude estimation [used by Stevens], one stimulus at a time is presented to a subject, who assigns it a number (greater than zero), which reflects its strength.
In cross modality matching, a subject adjusts one kind of stimulus to reflect the strength of test stimuli which are in a different modality. For example, a subject could adjust the brightness of a color patch to match the loudness of a tone.
Pitch scaling experiment