Forced Choice
and miscellaneous consideration


A variation for the presentation of trials in the method of constant stimulus (and other psychophysical techniques) is the use of forced choice.

In forced choice, the subject is presented with a number of spatial or temporal alternatives in each trial in which the stimulus is presented. The subject is forced to choose the location or interval in which the stimulus occurred.

For example, in the experiment of Hecht, Schlaer, and Pirenne, they could have implemented a two alternative forced choice (2AFC) procedure. For their experiment, two temporal alternatives could be presented to the subject for each trial, and the subject would have to choose which interval the flash was contained in. A schematic representation of a trial is presented below:

Each of the two intervals is preceded by a signal, a beep, which indicates the intervals. The flash is presented randomly in either the first or second interval. The subject's task is to respond with which interval the flash was presented in.

As before, the psychometric function is plotted. The percentage of correct responses (as opposed to the percentage of detection) is plotted against stimulus intensity. In the 2AFC procedure, the percentages range from 50% to 100% as compared to 0% to 100% in the regular MCS psychometric function. That is because as the stimulus becomes too dim to detect the subject is guessing which interval the flash was in. The guessing rate is 50% for two alternatives. Threshold values may now be determined from the plot by arbitrarily selecting, say 75%, as the threshold value.

In a two spatial alternative forced choice, there may be two locations in the stimulus field in which a flash may occur. The subjects task would be to choose the spatial location. This would not be appropriate for the Hecht, Schlaer, and Pirenne experiment. Can you figure out why?

Psychometric Function

Because guessing will lead to a percentage of correct responses equal to the reciprocal of the number of alternatives, the level at which threshold is defined must be adjusted for chance. In the curve below, plotting the psychometric function for a 2AFC experiment, the threshold is defined as 75% correct. This corresponds to a 50% threshold in a psychometric function derived from a yes/no detection experiment.

You can use the following equation to adjust for the probability of chance guessing:



p=corrected probability

p'=raw probability

C=probability of chance success

(For 2AFC, C = 0.5, so p'= 0.75 leads to a p = 0.5.)


Confounding Cues

It is important that the subject makes his choice (or guess) based on the proper criterion, in this case, the detection of a flash. Let's imagine that when a flash is presented, a shutter opens and closes causing the flash. If this shutter is audible, it can be used as a cue to the subject that a flash occurred in a particular interval regardless of whether or not the subject saw the flash. It is possible that the subject could pick up on a cue like this without even being aware of it (especially if there is feedback, see below). Such a situation arose in an experiment I was working on. My solution was to add "dummy" shutters that would go off in both intervals.

In this technique (and others that use discrete stimulus trials) it is possible to have the subjects set the pace of the experiment. You can have the subjects press a button that starts a trial. This way subjects can get ready for a trial and have time to blink or yawn or whatever so that it will not interfere with the data collection. It is also possible to include a "Do over" button. If a subject missed a trial either do to blinking, inattention, or falling asleep, he can re-present the trial. "Do over" buttons can be dangerous if subjects use them to try to get the "right" answer instead of using them appropriately. A "do over" button can also be helpful for trials in which the subject gave a particular response by accident. For example, the subject meant to hit the button indicating interval 1, but missed and hit the interval 2 button.

When working close to threshold, it may be frustrating for subjects because they may hardly ever really "see" the stimulus. Sometimes trials that are easy to detect can be thrown in to relieve this frustration, however these trials are not used for analysis.

Blinks and Inattention

Similarly to the discussion of response bias on the previous page, subjects may make incorrect responses due to inattention and blinks (that is, they missed the stimulus for reasons other than it being undetectable).

Instead of the "do-over" button, the following equation can be used to correct the psychometric function for these trials. You must assume a certain rate for missed trials. This rate is usually small, for example 1% (rho = 0.01) of the trials are missed.


where p=corrected probability,
p'=raw probability,
C=probability of chance success,
rho=probability of lapses in attention, misdirection of
  the eye, blinks, etc.


This procedure can be made more "enjoyable" for the subject with the addition of feedback. After each trial, you can signal to the subject whether they chose the correct alternative. This helps maintain a stable criterion and the feedback helps the subject maintain vigilance for the stimuli. Combined with self-pacing, the experiment can be quite bearable for the subject.

The benefits of forced choice include the aspect of greater subject "enjoyableness" especially when combined with feedback and the control of self-pacing. At first many subjects are reticent to guessing, but in general they like it better than difficult yes/no judgments. (Actually, it is quite surprising how many "correct" responses subjects give even though they may not be "consciously" aware of the stimulus.) Forced choice is the best way to maintain stable and low criteria in an experiment. This makes the results more valid. Standard packages, such as SAS, can handle forced choice in probit analysis.

The drawbacks to forced-choice are the difficulty in setting up the procedure. There are still errors of habituation and expectation, but they are decreased.

Additional Considerations

Forced choice can be used instead of yes/no in the Method of Limits as well as the MCS. They can also be used in staircase procedures, which are modified versions of the Method of Limits. Staircases will be described later in this chapter. In general, you should try to use forced choice because of all its benefits.

Many times people confuse forced choice with pass/fail, greater/less than, or same/different judgments when a standard (or original) is presented along with the test stimulus. This is because the subjects have to (they are forced to) make a decision about the test stimulus relative to the standard. However this is not forced choice. In forced choice, there are alternatives between which you must choose. The lowest probability on the psychometric function is the chance of correct guessing. For pass/fail, greater/less than, or same/different judgments, the probabilities of the response still range from 0% to 100%. Keep this in mind when designing, analyzing, and describing your experiments.


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