Given a repeated signal (identical on all presentations) which is barely perceptable to an observer, the observer will only sometimes respond that a signal was present.

Different types of scales are used for different properties; these reflect how precisely the differences between stimuli are measured. These scales have been used to derive equations relating the perceived strength of various kinds of stimuli to their absolute strength.

In this method, the experimenter presents stimuli in random order. The standard stimulus may be presented first and remembered, or may be presented on each trial. The subject judges whether each comparison stimulus is larger or smaller than the standard stimulus.

In this example, the subject is asked "Is the comparison stimulus larger than the standard stimulus?", and answers "Yes" or "No". The stimuli are presented in blocks, with each stimuli strength appearing once in each block. The numbers in parenthesis show the order of presentation of stimuli within each block. The proportions of "Yes" responses are then calculated for each signal strength, and graphed. The threshold of equality is defined as the signal strength corresponding to the 50% level of "Yes" responses. (With more data, the interpolation would be more precise.)

Stimulus strength | Block 1 | Block 2 | Block 3 | Prop. of "Yes" | |

10 | n (3) | n (8) | n (5) | 0 / 3 | |

20 | n (8) | n (1) | n (6) | 0 / 3 | |

30 | n (6) | n (2) | n (9) | 0 / 3 | |

40 | n (5) | n (4) | n (4) | 0 / 3 | |

50 | n (1) | n (9) | Y (2) | 1 / 3 | |

60 | Y (7) | Y (5) | Y (1) | 3 / 3 | |

70 | Y (9) | Y (3) | Y (3) | 3 / 3 | |

80 | Y (2) | Y (7) | Y (8) | 3 / 3 | |

90 | Y (4) | Y (6) | Y (7) | 3 / 3 | |

In this method, the experimenter changes the strength of the stimulus in large steps initially, then in smaller steps as the equality point is approached. (These steps can be made as small as desired, to produce an actual measure of perceived equality, but the procedure will be shown here in large steps to be comparable to the previous method.) This method is more efficient than constant stimuli, because some comparison stimuli are never presented. [This is the basic idea behind "adaptive testing", a recently added option on the GRE.]

In this example, the subject is asked "Is the comparison stimulus larger than the standard stimulus?", and responds "Yes" or "No". The sequence of stimuli presentation is somewhat complicated because it depends on the responses of the subject. The numbers in parenthesis show the order of stimuli presentation within each trial. Some stimuli are never presented, because it is assumed that the subject's response can be derived from the other responses. These cells in the table have only "Y" or "n".

Stimulus Strength | Trial 1 | Trial 2 | Trial 3 | Prop. of "Yes" | |

10 | n (1) | n | n | 0 / 3 | |

20 | n | n | n (1) | 0 / 3 | |

30 | n | n | n | 0 / 3 | |

40 | n | n (2) | n (3) | 0 / 3 | |

50 | n (2) n (5) | n (4) | Y (4) | 1 / 3 | |

60 | Y (6) | Y (3) | Y (2) | 3 / 3 | |

70 | Y (4) | Y | Y | 3 / 3 | |

80 | Y | Y (1) | Y | 3 / 3 | |

90 | Y (3) | Y | Y | 3 / 3 | |

The first trial, in detail:

The first comparison stimuli presented is 10 units, much weaker than the standard; when the subject responds "No",

the second comparison presented is 50 units (40 units stronger than the first). When the subject again responds "No",

the third comparison presented is 90 units (40 units stronger than the second). This is now too strong, so the subject responds "Yes". At this point, we know the subject's point of equality is between 50 and 90, so we will reduce the step size to get a better estimate, and begin decreasing the strength of the stimuli.

The fourth comparison is 70 units (20 units weaker than the third), but is still stronger than the standard; the subject responds "Yes",

and the fifth comparison is 50 units (20 units weaker than the fourth). This is the same strength as the third comparison, but because the step size is smaller, we have gained information; when the subject responds "No", we know that the point of equality is between 50 and 70.

The sixth comparison is 60 units (10 units stronger than the fifth), and the subject responds "Yes". This shows the point of equality to be between 50 and 60, and the trial ends.

(To find a smaller interval, the step size would again decrease, and the procedure would continue.)

All blank cells below 60 are now labelled "No", and those above 60 are labelled "Yes". The calculation of the point of equality then proceeds as above.

This method allows the subject to adjust each comparison stimulus until it appears equal to the standard. The table responses are then filled in, "No" below the equality point, and "Yes" above.

Stimulus Strength | Block 1 | Trial 2 | Trial 3 | Prop. of "Yes" | |

10 | n (1) | n | n (1) | 0 / 3 | |

20 | n (2) | n | n (2) | 0 / 3 | |

30 | n (3) | n | n (3) | 0 / 3 | |

40 | n (4) | n | n (4) | 0 / 3 | |

50 | n (5) | n (5) | Y (5) | 1 / 3 | |

60 | Y (6) | Y (4) | Y | 3 / 3 | |

70 | Y | Y (3) | Y | 3 / 3 | |

80 | Y | Y (2) | Y | 3 / 3 | |

90 | Y | Y (1) | Y | 3 / 3 | |

This method is similar to the method of adjustment, except that the experimenter controls the presentation of the stimuli, and the subject responds "Yes", "No", or "Equal". This example is presented analogously to the three above; the procedure can be more powerfully used be estimating both the upper and lower thresholds of discriminability, instead of the equality point.

Stimulus strength | Trial 1 | Trial 2 | Trial 3 | Prop. of "Yes" | |

10 | n (1) | n | n (1) | 0 / 3 | |

20 | n (2) | n | n (2) | 0 / 3 | |

30 | n (3) | n | n (3) | 0 / 3 | |

40 | n (4) | n | = (4) | 0 / 3 | |

50 | = (5) | = (5) | Y (5) | 1 / 3 | |

60 | Y (6) | Y (4) | Y | 3 / 3 | |

70 | Y | Y (3) | Y | 3 / 3 | |

80 | Y | Y (2) | Y | 3 / 3 | |

90 | Y | Y (1) | Y | 3 / 3 | |

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