Science, Maths & Technology

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# 9.2.1 Method of limits

To determine an auditory threshold using the method of limits, one would begin with an undetectable stimulus and then gradually increase the intensity until the subject detects it. Results from a hypothetical method of limits study are shown in Table 1. Stimulus intensity is shown in the first column and the subject's response to each stimulus is listed under ‘trial 1’. Only when the stimulus was 14 dB SPL, did the subject respond ‘yes’ (I can hear the stimulus). The threshold for hearing the stimulus therefore lies somewhere between 13.5 and 14.0 dB SPL. Column 3 shows a repeat of the experiment. You can see that the responses of the subject in trial 2 were not the same as in trial 1. In this case the subject failed to detect the stimulus at a level of 14 dB SPL. As the experiment is repeated (trial 3 and trial 4) the responses differ from trial to trial. Loud stimuli, at intensities of 15 dB SPL and above are always heard whereas very soft stimuli (13 dB SPL and below) are never heard. Between these extremes, responses vary and are heard only a certain percentage of the time: stimuli at a level of 14.5 dB SPL were heard in 3 out of 4 trials (75%), whereas a stimulus level of 13.5 dB SPL was heard in only 1 out of 4 trials (25%). The reason why responses may differ is because actual thresholds change from trial to trial or because there is a variable amount of extraneous ‘noise’. We shall return to this problem later. The percentage detection for each stimulus is shown in the last column. If we plot the percentage of stimuli detected against stimulus intensity we get a graph similar to that shown in Figure 33 – a smooth S-shaped curve known as a psychometric function. It is usual to define the threshold stimulus as that stimulus intensity corresponding to a 50% detection on the psychometric function.

## Activity

In this case, what is threshold for our subject?

According to the graph, a 50% detection corresponds to a signal intensity of 14.0 dB SPL.

Table 1 Results from a hypothetical method of limits study.“yes” responses (%)
Stimulus/dB SPLtrial 1trial 2trial 3trial 4% detection
12.0NNNN0
12.5NNNN0
13.0NNNN0
13.5NNYN25
14.0YNYN50
14.5YYYN75
15.0YYYY100
15.5YYYY100
16.0YYYY100
16.5YYYY100
17.0YYYY100
Figure 33 A typical threshold function. By convention, absolute threshold is defined as the intensity at which the stimulus is detected 50% of the time

Although very useful, the method of limits is open to various sources of bias and error. One of its drawbacks is that the change in stimulus intensity (increase or decrease) is orderly and regular.

## Activity

How may this affect the observer?