changes of sensitivity and criterion. For this basic simulation, 5,000 trials were generated, half of which contained a signal and the other half noise. On each trial, a stimulus was presented that contained either only noise or a signal embedded in noise and the observer determined whether the signal was absent or present. The internal response on each trial was (randomly) drawn from one of two Gaussian distributions. For the noise stimulus (dark grey), a distribution was constructed (noise distribution) that centred around a mean of 0 with a variance of 1. For the signal-embedded-in-noise stimulus (red), a distribution was created (signal distribution) that centred around a mean of d’ = 1.14 (observer detection sensitivity) with a variance of 1 (Figure 7.3.1A), 0.75 (Figure 7.3.1B) or 1.25 (Figure 7.3.1B). The x-axis in Figure 7.3.1 indicates the strength of the internal response, which varied between -4 and 5, where 0 can be thought as a baseline, above which the likelihood that the signal is detected increases with response strength. The y-axis indicates the counts of each type of internal response. Because it is a 2AFC task, it assumed that there is no response bias (i.e., observers do not prefer one response over the other). This means the decision criterion reflects the intersection of the two internal response distributions (blue line).
Figure 7.3.1 Modulations of the signal distribution. (A) Signal detection theory assumes that the internal response distribution to noise and signal are Gaussian with similar variance but different means. In this simulation, the noise distribution always centres around a mean of 0 and the signal distribution around a mean of d’ = 1.13. Because it is a 2AFC task, we assume no response bias, c ≈ 0. (B) In the case where the signal distribution has a variance smaller than that of the noise distribution, the hit rate will increase, p(H) = 0.86, without changes to the false alarms, p(FA) = 0.20. (C) If the signal distribution has a greater variance than the noise
distribution, the hit rate will decrease, p(H) = 0.73, but the false alarm rate remains the same, p(FA) = 0.21. In both cases (B&C) criterion and sensitivity will change.
In Figure 7.3.1A, the variance of the signal distribution equals that of the noise distribution. This results in a hit rate of 0.79 and a false alarm rate of 0.21 which, in turn, yield a d’ value close to the one injected (i.e., d’ = 1.14) and a value of c that suggests there was no response bias. In Figure 7.3.1B, the variance of the signal
distribution was decreased (𝜎signal = 0.75), following which the hit rate increased, p(H) = 0.86, but the false alarm rate remains more or less unchanged, p(FA) = 0.20. These changes are reflected by a shift in criterion (c = -0.12) and an increase in sensitivity. In Figure 7.3.1C, the variance of the signal distribution was increased (𝜎signal = 1.25), which induced a decrease in hit rate, p(H) = 0.73, but left the false alarm rate practically the same, p(FA) = 0.21. This, in turn, shifted the criterion in the opposite direction (c = 0.091) and decreased sensitivity (d’ = 1.01).
Essentially, modulations of the signal distribution lead to changes in both criterion and sensitivity. By contrast, a shift of the criterion without changes to the signal distribution will alter the number of both hits and false alarms, such that sensitivity is minimally affected. However, the results in Figure 4.2.5H and Figure 4.2.5I suggested that sensitivity might have oscillated but in opposite phase, so that the oscillations cancelled each other out when pooled together. Furthermore, a mere criterion shift without changes to the signal distribution typically reflects a change in observer decision strategy. It does not seem reasonable that observer decision strategy fluctuates from trial to trial. More likely, the oscillation observed in criterion reflects fluctuations in perceptual bias, which is captured by the modulations of the signal distribution in Figure 7.3.1.
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