Research Methods


Demonstration 2.1 Using the Method of Limits to Determine Absolute Threshold
Demonstration 2.2 Using the Method of Constant Stimuli to Determine Absolute Threshold
Demonstration 2.3 Understanding the Noise and Signal+Noise Distributions in Signal Detection Theory
Demonstration 2.4 Understanding ROC Curves in Signal Detection Theory
Demonstration 2.5 Using Magnitude Estimation

Before You Start

• You may have heard Earl Babbie's distinction between the "Hard" sciences and the "Easy" sciences (as opposed to the more common "Hard" and "Soft" sciences). What places psychology squarely among the "Hard" sciences is the complexity of measuring concepts of interest. One advantage of studying perception is that the physical stimuli of interest often can be measured quite precisely. Nonetheless, the psychological reaction to those stimuli is not so easily measured. Consider the enduring contribution of Fechner to the field of perception and to psychology as a discipline. By believing that psychological experience could be measured and then developing procedures for that measurement, Fechner and the psychophysicists that followed him have made enormous contributions to the field of psychology.

• Measurement in perception provides a microcosm of the problem facing measurement in psychology. That is, we are really interested in knowing about what goes on in a person's mind (e.g., how bright is this light? does this gift make you happy?). However, we cannot directly access the mind, so we must rely on some form of behavior (e.g., self-report or physiological measurement).

• Consistent with Theme 2, you should consider the exquisite sensitivity of your perceptual systems (in terms of absolute thresholds) and the contributions of context to judgments.

• Consistent with Theme 3, you'll note in this chapter that the identical stimulus can give rise to very different perceptions. And different stimuli can give rise to perceptions that don't differ. Even though stimuli are ambiguous in many ways, we manage to perceive the world with sufficient clarity that we are often unaware of the ambiguity.

• Especially as you consider Signal Detection Theory, think of the role that cognitive processes play in the perception of stimuli (Theme 4). Moreover, the context effects on judgments found in other psychophysical methods (e. g., impact of prior stimuli) also indicate the important role of cognitive processes.

Measuring Responses to Low-Intensity Stimuli

Classical Psychophysical Measurement of Detection

• Gustav Theodor Fechner (1801 - 1887) documented the classical methods of psychophysics in his seminal text, The Elements of Psychophysics (1860). In each of the three methods discussed below, one would be attempting to locate an absolute threshold (also called an absolute limen). Such a threshold represents the stimulus intensity at which a person can just barely detect a stimulus. Thus, presumably, at lower intensities (subliminal) a person would not be able to detect the stimulus and at higher intensities (supraliminal) a person would always be able to detect the stimulus. Research has determined that the threshold cannot be so precisely determined. In fact, some people question the very concept of a threshold (see Signal Detection Theory).

Method of Limits

• This method is simple, but you need to worry about two kinds of errors: habituation and anticipation. With habituation, a person may continue provide the same response, even though the person can perceive a change. With anticipation, a person may change her or his response, even though the person cannot really perceive a change. To offset the effects of these errors, you present two different types of series to each person. The series will either be ascending (from a sub-threshold stimulus to increasingly intense stimuli) or descending (from a supra-threshold stimulus to increasingly less intense stimuli). Because the participant may attempt to memorize a pattern of responses, it is also prudent to begin the series from different starting points. Demonstration 2.1 illustrates the use of the Method of Limits.

Demonstration 2.1 Using the Method of Limits to Determine Absolute Threshold This demonstration involves detecting sweetness (sugar) in water. (You may want to try a variant using other sweeteners.) Once you have the materials prepared, save them to use for Demonstration 2.2. First, collect 10 16 oz plastic cups and label them (presuming that your participant will be blindfolded, here they are labeled 1 through 10). You'll also need measuring spoons (.25, .5, and 1 teaspoon).

Photo by H. Foley

Use the measuring spoons to add the following amounts of sugar to each cup: Cup 1 = .25 teaspoon, Cup 2 = .5 teaspoon, Cup 3 = .75 teaspoon, Cup 4 = 1 teaspoon, Cup 5 = 1.25 teaspoon, Cup 6 = 1.5 teaspoon, Cup 7 = 1.75 teaspoon, Cup 8 = 2.0 teaspoons, Cup 9 = 2.25 teaspoons, and Cup 10 = 2.50 teaspoons. Next, add water to each of the cups to bring the amount of water in each cup to the same level (roughly 16 ounces, or use a measuring cup). Stir the contents of each cup to thoroughly distribute the sugar.

Photo by H. Foley

You're now ready to conduct a psychophysical study of sweetness detection using the method of limits (and also the method of constant stimuli in Demonstration 2.2). To collect your participant's responses, first download the Response Sheet. Follow the instructions on the Response Sheet to determine the absolute threshold. To conduct this demonstration with a class, give each student an empty plastic cup and pour a small amount from the appropriate numbered cup into the empty cup. Once the student has rated that stimulus, go on to the next numbered cup in the sequence.

Method of Constant Stimuli

• With this method (illustrated in Demonstration 2.2 below), stimuli are presented in a pre-determined random order, so there is no concern about habituation or anticipation errors.

Demonstration 2.2 Using the Method of Constant Stimuli to Determine Absolute Threshold As long as you have your participant blindfolded and all the stimuli (from Demonstration 2.1), you should conduct this demonstration as well. First, download the Response Sheet. Follow the instructions on the Response Sheet to determine the absolute threshold.

Method of Adjustment

• With this method, the participant is in control of adjusting the levels of the stimulus. The method doesn't work so readily with the sweetness demonstrations that we used for the Method of Limits and the Method of Constant Stimuli (because the participant can't easily remove sugar from the solution). You could imagine the participant controlling a knob that changed the loudness of a sound. The experimenter might initially set the loudness level below the participant's threshold. The participant would then adjust the knob to turn the sound level up and then down (and up and down, etc.) until reaching the level at which the stimulus is just barely detectable.

Signal Detection Theory

The classical psychophysical methods search for a threshold (e. g., an absolute threshold), but for signal detection theory there is no threshold. Instead, there are two important concepts: the respondent's criterion and the sensitivity of the respondent (d').

Unlike the classical psychophysical methods, for a signal detection study only two kinds of trials are used (Noise and Signal+Noise). [Note that the Noise trials are equivalent to the "catch trials" in a classical psychophysical study, in that no signal is present. In the classical psychophysical methods a signal of some level is present on each trial.] Because there are only the two kinds of trials, the Signal+Noise trials must be confusable with the Noise trials, so the signal level mustn't be much greater than the noise level.

The actual shape of the distributions is crucial, but for simplicity's sake, we'll assume a normal distribution. If you've taken a statistics course, you know all about the way to translate z-scores into proportions of a normal curve and vice versa (proportions into z-scores). You may want to brush up on z-scores and the normal distribution, because it will give you a deeper understanding of signal detection theory.

Let's first consider the typical 2x2 table illustrating an observer's responses and the actual state of a trial. (And, if you remember your statistics course, this table should remind you over Type I and Type II Errors.)

  Says "Yes" Says "No"
Signal Present
Signal Absent
False Alarm
Correct Rejection

Now let's focus on the Noise (Signal Absent) distribution. Over a number of Noise trials (e.g., 100), a person will make a number of false alarms (e.g., 30) and correct rejections (e.g., 70), both of which are to be found in this distribution. [Note the complementarity of false alarms and correct rejections, so that we need know only one--so we'll focus on false alarms.] Can you determine roughly where the participant's criterion must have been so that 70% of the distribution is to the left of the criterion (saying "no" when no stimulus was present) and 30% of the distribution is to the right of the criterion (saying "yes" when no stimulus was present)?

Now let's turn our attention to the Signal+Noise (Signal Present) distribution. Over a number of Signal+Noise trials (e.g., 100), a person will make a number of hits (e.g., 85) and misses (e.g., 15), both of which are to be found in this distribution. [Note, again, that these two terms are complementary, so we need know only one--so we'll focus on hits.] Can you determine roughly where the participant's criterion must have been so that 85% of the distribution is to the right of the criterion (saying "yes" when a stimulus was present) and 15% of the distribution is to the left of the criterion (saying "no" when a signal was present)?

To ensure that you understand the concepts, you may want to print out the two distributions above and then draw in the criterion line for each distribution. The magic happens once you realize that the participant has only one criterion, which means that you can line up the criterion lines for the two distributions, superimposing the Signal+Noise distribution on the Noise distribution, as seen below. In so doing, you will have defined the separation between the two distributions (d').

In the demonstration below, you'll have the opportunity to examine different combinations of percentages of hits and false alarms. At this point, it should be clear to you that if the hit and false alarm percentages are the same (e.g., both 80%), the two distributions must be completely overlapping (thus d' = 0). Moreover, as the false alarm percentage becomes increasingly small and the hit percentage becomes increasingly large, sensitivity becomes increasingly large (thus d' would be high).

Link - David Heeger (NYU) has a nice summary page for Signal Detection Theory.

Demonstration 2.3 Understanding the Noise and Signal+Noise Distributions in Signal Detection Theory Generous colleagues have provided demonstrations of signal detection theory on the web. Below are a number of links to wonderful demonstrations of the interplay of criterion and d'. Here, I'll provide a decidedly low-tech approach to understanding the underpinnings of signal detection theory. Download the Word file on Signal Detection and be sure that you can completely answer all parts of the exercise. (Use the second page for Demonstration 2.4.)

Link - Indiana University's Cognitive Science Program has several on-line experiments, including a neat and complete Signal Detection experiment.

Link - Ann Bisantz (SUNY Buffalo) has developed a very useful illustration of the interplay of criterion and d' (as well as the variance of the two distributions). Note that the ROC curve is displayed as well.

Link - John Krantz (Hanover College) has developed a useful tutorial for signal detection theory.

Link - Here is a brief Introduction to Signal Detection Theory that includes a Java applet illustrating how d' varies in a ROC curve with different probabilities of Hits and False Alarms (Claremont Graduate University's Web Interface for Statistics Education).

Link - Thomas Wickens (UC Berkeley) has provided a number of useful programs (Windows only) for signal detection analysis.

Demonstration 2.4 Understanding ROC Curves in Signal Detection Theory Using the Word document for the above demonstration, plot each of the points on the ROC Curve. The links above will also allow you to see how d' is determined when you plot the points given by p(Hit) and p(False Alarm). In general, as points move toward the upper left of the figure, d' becomes larger. As the points move toward the diagonal line (d' = 0), sensitivity decreases. Moreover, note that a number of points populate each d' curve, which illustrates the fact that people with equal sensitivity may have different criteria. On any given curve, points to the left indicate more conservative criteria (people who are less willing to say "yes") and points to the right indicate more liberal criteria (people who are more willing to say "yes").

Forensic Applications of Signal Detection Theory

• There are a number of forensic applications of signal detection theory. For instance, you can think of a trial in signal detection terms.

  Jury Convicts Jury Acquits
Defendant is Guilty
Defendant is Innocent
False Alarm
Correct Rejection

Presumably, our judicial system is biased to avoid false alarms (convicting innocent defendants), which is a criterion issue. That is, in signal detection terms, we would expect a very conservative criterion to operate in the courtroom. If there is little sensitivity involved (i.e., the evidence is not particularly strong), a conservative criterion will not only minimize false alarms, but also it will minimize hits -- thereby letting guilty people go free. As you are probably aware, in spite of this presumed bias toward a conservative criterion, the judicial system still manages to convict many innocent people. In some cases, the crimes for which those people were convicted are so serious that the innocent people ended up on death row. Furthermore, it's quite likely that innocent people have been executed.

Link - The Justice Project maintains a site that will inform you about wrongful convictions. They have also published a report on eyewitness testimony. Another site to peruse is the Truth in Justice site.

•As discussed in the textbook, one important application of signal detection theory is in the evaluation of eyewitness identification. Whether dealing with an actual lineup or a photo-array (and many researchers use the term "lineup" for both types of eyewitness scenarios), you should be able to place this issue in signal detection terms.

  Witness says "It's Him/Her " Witness says "It's Not Him/Her "
Eyewitness Looks at Criminal
Eyewitness Looks at Non-Criminal
False Alarm
Correct Rejection

As always in the signal detection paradigm, both sensitivity and criterion are important in determining performance. Think through the factors that might influence both sensitivity and criteria. What might a person do to increase the sensitivity of an eyewitness about to experience a lineup? What might a person do to increase the likelihood that an eyewitness will choose a person from the lineup? What kind of criterion would that be (more liberal or more conservative)? Would it be "fair" to manipulate sensitivity and criteria in these ways?

Link - Roy Malpass (University of Texas El Paso) has a site that contains a wealth of information about eyewitness research. Pay particular attention to the section on biased lineups.

Link - Gary Wells (Iowa State) has another useful site, including an opportunity to assess your own eyewitness abilities. From this site you can also download the National Institute of Justice report: Eyewitness evidence: A guide for law enforcement. The National Institute of Justice has also published Eyewitness evidence: A trainer's manual for law enforcement.

Link - Steven Penrod (John Jay) is another major researcher in this area, so you'll find his site a helpful compendium of research papers.

Two-Alternative Forced Choice Procedure


Measuring Responses to More Intense Stimuli

Classical Psychophysical Measurement of Discrimination

Link - Hiroshi Ono (York) has provided a web version of his HyperCard stack (Precision & Accuracy). Visiting this site will give you the opportunity to learn about all three classical methods in the context of discrimination. You'll also learn about Weber's Law. All in all, this is probably the best site for learning about classical psychophysical methods.

Method of Limits for Measuring Discrimination

Method of Constant Stimuli for Measuring Discrimination

Link - You can run an experiment to determine the jnd for line length at the USD Internet Sensation and Perception Laboratory.

Method of Adjustment for Measuring Discrimination

Relationship between Physical Stimuli and Psychological Responses

Weber's Law

Fechner's Law

Stevens's Power Law

Demonstration 2.5 Using Magnitude Estimation Before you begin, print out the response sheet. In this exercise, you'll see a series of squares that vary in size. As each square appears on the screen, write a number on your response sheet that seems to best describe the size of the square. You should freely use any non-zero number, so fractions, decimals, and multi-digit numbers are all acceptable as long as they adequately reflect how large the square seems to you. When you're ready to begin, click on START. When you've made all twelve magnitude estimations, print out the scoring sheet.

Measuring Brain Activity Due to Perceptual Stimuli

Studying Individual Neurons

Studying Massed Brain Activity

Link - David Heeger (NYU) has provided an example of fMRI detecting activity in different areas of visual cortex.


Test Yourself

1. Describe how psychophysics might be relevant if you wanted to examine low-intensity stimuli in each of the following areas: vision, hearing, touch, pain, smell, and taste. In each case, briefly describe how you would use the method of limits (or an appropriate modification), the method of adjustment, and the method of constant stimuli to measure a detection threshold.

2. Why do we need both ascending trials and descending trials in the method of limits? Why don’t we need to worry about the two kinds of trials in the method of constant stimuli? Similarly, why do we need to vary the stimulus with which we begin using the methods of limits, and why is this precaution unnecessary when using the method of constant stimuli?

3. Describe the advantages and disadvantages of each of the three classical psychophysics methods, illustrating each method with an example from vision.

4. Suppose you are standing near an electric coffee urn, waiting for the red light to turn on to indicate that the coffee is ready. Apply signal detection theory to the situation, describing aspects of sensitivity and criterion. Now describe the four possible outcomes in this situation with respect to the occurrence of the signal and your response.

5. The following questions apply to ROC curves:
      a. If d’ is large, is the probability of a hit larger or smaller than if d’ is small?
      b. What does d’ measure?
      c. Suppose that Tuan has a d’ of .5 and Ramón has a d’ of 1.5. If they have the same hit rate, which of them has the higher false alarm rate?
      d. How is a particular point on an ROC curve related to the location of the criterion line in the probability distributions in Figure 2.5 from the textbook?

6. Why might signal detection theory be useful for research on eyewitness testimony? What would be the likely effect on d’ of creating a lineup of people who were very similar in appearance? Suppose that the typical d’ for eyewitness identification is 1.0. What would be the impact on hits and false alarms if you set a very conservative criterion?

7. Describe how you could use each of the three classical psychophysics methods to measure color discrimination. Then discuss how psychophysics might be relevant if you wanted to examine high-intensity stimuli in each of the areas mentioned in Question 1 (in addition to color discrimination). Mention both discrimination studies and studies concerning the relationship between physical stimuli and psychological responses.

8. Which is heavier, a pound of iron or a pound of feathers? Younger children might pause before answering, and might even answer incorrectly. Why? They are probably thinking which would feel heavier, rather than which would be heavier. How would you determine the Weber fraction for the weight of iron and for feathers? What would it mean if they were different?

9. The section on the relationship between physical stimuli and psychological reactions ended with a statement that a change in the physical stimulus is typically translated into either a magnified or a diminished change in the psychological reaction. Discuss this statement with reference to Fechner and Stevens.

10. If you wanted to learn about perception in humans, what role might the psychophysical methods play? What role might physiological methods (e.g., EEG, fMRI) play? Do you think that it is essential to fully understand brain function to develop an adequate theory of perception?

Teaching Materials

Lafayette Instrument Co. produces the Light Discrimination Apparatus (Model 14011), which is useful for demonstrating a variety of psychophysical methods. It may also be used to illustrate the effect of context (class will typically report that lights are not on when set to a low level and classroom lights are on -- then turn off the classroom lights). They also sell a set of weights that can be used for psychophysical testing, as well as aesthesiometers for testing two-point thresholds.

Psychology Software Inc., Laboratory in Cognition and Perception (Windows only). This package of demonstrations, developed by C. Michael Levy and Sarah E. Ransdell, contains a number of useful tools for teaching perception. For the purposes of this chapter, they present demonstrations of classical psychophysical and signal detection methods.

Walter Beagley (Alma College) has developed Eye Lines, which still works on non-Intel Macs and PCs. The package is quite useful for a variety of purposes, including using classical psychophysical methods to assess the magnitude of illusions. Keep your eyes open for a forthcoming revision to the program.

Thomson Higher Education has published two very useful CD-ROMs. John Baro (Polyhedron Learning Media) has developed Insight: A Media Lab in Experimental Psychology [see Measuring Illusions and Signal Detection] and Colin Ryan (James Cook University) has developed Exploring Perception [see Module 5].

Link - Michael Mann (University of Nebraska) has placed his physiology textbook online, and it includes a chapter (Chapter 2) that discusses psychophysics.

Recommended Readings

Baird, J. C. (1997). Sensation and judgment: Complementarity theory of psychophysics. Erlbaum.

Gescheider, G. A. (1997). Psychophysics: The fundamentals (3rd Ed.). Erlbaum.

Macmillan, N. A. (2002). Signal detection theory. In H. Pashler (Ed.) Stevens's handbook of experimental psychology. Wiley.

Macmillan, N. A. & Creelman, C. D. (2005). Detection theory: A user's guide (2nd Ed.). Erlbaum.

Stevens, S. S. (1986). Psychophysics: Introduction to its perceptual, neural, and social prospects. Wiley.

Wickens, T. D. (2001). Elementary signal detection theory. Oxford.