Introduction to Scaling

How do we go about assigning numbers to psychological events so that we can use those numbers to stand in for the events. How do I go about setting up measurement methods so I can end up making statements like the following:

Through the course of therapy the client's ego structure has beome less threatened. I must measure the degree of threat.
Thus, the experimental treatment is seen to reliably and significantly reduce racial prejudice. I have to measure racial prejudice.
New Coffiest without caffeine tastes exactly like freshly perked coffee.
How hot is a hot pepper?
- Scoville College developed a hotness scale. Take a standard amount of the active ingredients in a pepper. Dilute the substance with water until you can no longer taste the hotness of the pepper. Jalapeno requires 3K (3,000) to 5K (5,000) times dilution to not taste hot.Scotch Bonnet requires 300K (300,000) times dilution to not taste hot.
- Paul Rozin, a psychologist who has researched ingestive behavior for many years argues that we like spicy-hot food because the oral receptors send "damage/pain" signals to the brain which then releases endorphins for a "feel good" high.
After you taste a food and decide to add salt, you generally have a pretty good idea of the amount of salt to add.

I. Basic Fact: Psychology is NOT warmed over physics.

There is no instrument available that can measure color. All the available instrucments can do is tell me how much energy is present in each wavelength; what the total amount of energy is; how the energy levels change from moment to moment. None of this really can tell me what color a person will report experiencing. Color is psychology; wavelengths and energy level is physics.

Likewise, when I measure brightness, the instrument I use is the eye. What happens is I use a photometer and I adjust a light in the photometer until it looks as bright as the surface I want to measure and then I read off the luminance level from how I had to set the light in the photometer. Without me doing the adjusting the phtometer wouldn't work.

There is no instrument at all that allows me to measure lightness except by comparing the lightness (white to balck) of an unknown against a series of graded grays. All an instrument can do is tell me how much light is being reflected or the percentage of light being reflected; it cannont tell me how white or gray or black that surface will look.

The same principle holds for loudness, or flavor, or verticality, or whatever expeience you wish. A physicist measures stimuli but we don't experience stimuli we experience sensations and it is those that we want to measure.

II. Scales based on liminal measures: Indirect scaling techniques

Gustav Fechner developed his scaling techniques from a consideration of the jnd. In these techniques the subject is never asked to tell how big the sensation is, instead we measure the DL ("Are these two stimuli the same or different?") and by using some fancy footwork end up with a scale that measures the intensity of the sensation. They are indict methods because we approach the scaling of intensity inderectly--from the sensitivity to change.

Weber's law:
- This law asks the question of what is the relationship between the just noticeable difference and the intensity of the standard stimulus. We know that the jnd for lifted wieght at 200 g is about 8 g. Is 8 g also a jnd at 100 g or at 1000 g? The answer is no! At 100 g the jnd is about 4 g and at 1000 g the jnd is about 40 g. As the more asture of you have recognized, the jnd for lifted weight, in the examples given runs at about 4% of the standard stimulus. Two weights which differ by 5% will be just noticeably different. Weber's law simply says that the ratio of the jnd to the standard stimulus is constant. The "ÆS" simply means the increment in stimulus that is just noticeably different--for Weber's law it is not any increment in stimuluation.
- Different sense modalities have different Weber constants. The keener the sense the larger the ratio and the smaller the decimal equivalent
  - For lifted weights the Weber constant is about 0.03.
  - For pitch the Weber constant is about 0.003.
  - For saltiness, the Weber constant is about 0.3.


(These figures adapted from someplace. I thought they were from Woodworth & Schlosberg, 1954. If you recognize them, please email me so I can credit the author.)

Weber's law, at best, is only roughly accurate and then only in the midrange of stimulaiton. It's sort of like Hookes' law in physics. Hookes' law tells how much a spring will stretch for each g we add at the bottom, but the law only holds for total weights that are neighter too large or too small.

Weber's law is only valid, if then, only when the standard stimulus is neither too large or too small. If we were to plot the size of the Weber constant for a wide range of stimuli we might find:

This figure shows that we require the smallest percentage change to detect a difference in a midrange of stimulation. If this were lifted weights, we might be outside the valid range when comparing postage stamp weights or weight-lifting barbells.

How does psychological Intensity increase with increases in stimulus intensity.

Its trivial to say that water tastes saltier and saltier as more NaCl is dissolved in it.

The question is "How much saltier does the water taste when I add more salt?

Y = mX
A constant increment in X produces a constant increment in Y. "m" describes the ratio of the two incrments.
Y = log X
A constant ratio change in X produces a constant increment (difference) in Y.
Y = Xn
A constant ratio change in X produces a constant ratio change in Y. "n" describes the ratio of the two sizes.

Every additional teaspoon of salt added to the water makes it taste the same amount saltier Every time I double the number of teaspoons the water becomes the same amount saltier. Every time I double the number of teaspoons the water increases its saltiness by the same ratio. For example each doubling of salt makes the water taste 10% saltier.

Fechner's answer is the middle choice: equal sensed differences correspond to equal stimulus ratios.


Y = mX A constant increment in X produces a constant increment in Y. "m" describes the ratio of the two incrments.	Y = log X A constant ratio change in X produces a constant increment (difference) in Y.	Y = Xn A constant ratio change in X produces a constant ratio change in Y. "n" describes the ratio of the two sizes.
Every additional teaspoon of salt added to the water makes it taste the same amount saltier	Every time I double the number of teaspoons the water becomes the same amount saltier.	Every time I double the number of teaspoons the water increases its saltiness by the same ratio. For example each doubling of salt makes the water taste 10% saltier.