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Background

The method of constant stimuli means that threshold is determined by presenting the observer with a set of stimuli of which some are above the threshold and of which some are below the threshold but that the set of stimuli are presented in a random order. This differs from the method of limits where stimuli are presented in fixed orders. In the method of constant stimuli, you always present all stimuli. This technique prevents the observer from being able to predict or anticipate what the next stimulus will be. However, the method of constant stimuli can be quite time-consuming. In the method of constant stimuli, the stimulus that is detected 50% of the time and not detected 50% of the time is considered to be the threshold (see the figure, Figure 2.4 from the book).
Illustration of threshold