Lab Session III:  Psychophysical Laws



  1. Purpose and Goals
    1. To illustrate how different people have described the relationship between the physical world and our experience, i.e., illustrate different proposed psychophysical laws
    2. To collect some data to allow us to test some of these laws
    3. To build on the foundations of the last two labs
  2. What is a scientific law?
    1. A description of a regularity observed in the data
    2. They do not imply an explanation for the regularity
  3. Weber's Law
    1. Developed to describe how JND's change as the background intensity changes
    2. This is an attempt to describe how our sensitivity to change relates to the intensity of the background stimulus
    3. Questions:
      1. Are all difference thresholds the same size regardless of the intensity of the background stimulus?
      2. If not, is there any systematic way that the size of these difference thresholds change?
    4. Weber answered these questions as: 
      1. No, thresholds get larger as the background intensity gets larger
      2. More than that, the JND increase at the same proportional rate as the background
      3. He summarized his statements with the following equation (it says exactly the same thing as above):



k is a constant.

I is the background intensity

ΔI is the difference between the intensity of the JND stimulus and background intensity

  1. Fechner's Law (Not in text)
    1. Review logarithms for yourself
    2. Observations:
      1. Fechner starts with Weber's Law
      2. Weber's Law suggests that we get progressively less sensitive to stimulus change as intensity increases
    3. Conjecture:
      1. What is Weber's Law refers not just to our ability to detect change but our overall sensitivity to stimuli
      2. In essence, threshold perception and suprathreshold perception are the same
    4. Leads to the following Law

      S is the strength of our sensory experience
      k is a constant and the same k as in Weber's Law
      I is the intensity of the stimulus

  2. Stevens' Power Law
    1. Starts with his development of Magnitude Estimation
    2. This is a direct measure of suprathreshold perception which is the object of Fechner's Law
    3. In many cases Fechner's Law is a reasonable fit for magnitude estimation data, say brightness or loudness
    4. In some cases, Fechner's Law does not fit at all, e.g., pain
    5. Stevens wanted a general law to cover all of the situations - that is one equation not a set of several
      • Science likes to use as general a description as is possible
    6. Stevens developed the following law, also called just the Power Law

      S and I are the same as for Fechner's Law
      c is a constant and can be anything
      b is the exponent that changes the shape of the function.  See the text for more.

Tasks Due for Next Week:

  1. Do the following experiments from Chapter 2 on the media website:
    1. Fechner vs. Stevens.
      1. No new data needs to be collected.  Use the data from both of last week's magnitude estimation experiments
    2. Weber's Law Experiment: Use Forced Choice: Frequency Discrimination: ISLE 2.8b
      1. Will Run 6 times
      2. On the Stimulus Settings Tab Change (once per run):
        1. Standard Frequency:
          • Lab 1 (AM): 100, 200, 400, 800, 1600, & 3200 Hz (This will be your I)
          • Lab 2 (PM): 200, 400, 800 1600, 3200, & 6400 Hz (This will be your I)
        2. Change no other settings
      3. On the Method Settings:
        1. Leave all the settings except:
        2. Maximum value of Frequency Difference (Hz): 75
      4. This is a Forced Choice method (Remember how to calculate these thresholds)
  2. Problems:
    1. Using the Magnitude Estimation Data from Week 2
      1. Paragraph describing procedure
      2. Use graph from last lab.  Does the graph fit better with Fechner's or Stevens' predictions?  Look at the shape.  Consider all of the data together.  Do not answer for each data set separately but the answer must apply to both results together.
    2. For Weber's Law Experiment : Method of Constant Stimuli: Frequency Discrimination
      1. Put data into the report.
      2. Calculate the JND for each standard frequency
        • Use the Forced Choice threshold equation
      3. Your JND will already be ΔI
      4. Convert to ΔI/I
      5. Plot on a bar graph (What Excel calls a column graph)
        • X axis = I (Standard Frequency (Hz))
        • Y axis = ΔI/I
      6. So 6 bars
      7. Answer the following question: Does the data fit Weber's Law or not?  Why or why not?
    3. Worth 25 points
    4. Point: Develop your skills at interpreting graphs, in particular, in how data relate to theoretical ideas.