Having defined the physical aspects of interest in our stimulus, we now turn to a consideration of the psychological factors that influence the measurement of perceptual sensitivity. How do we go about obtaining an estimate of a given observer’s sensitivity to global motion?
A simple approach
A simple way would be to present an observer with multiple examples of the stimulus with a particular global motion direction and coherence. On each presentation (‘trial’), the observer is required to say whether they could see the global motion or not. We could then summarise their performance by dividing the number of times they said “yes, I could see the global motion” by the number of trials that were performed.
For example, I could show you 10 examples of a rightward motion stimulus with 50% coherence, each with a new random set of dots, and each time ask you to respond “yes” or “no” regarding whether you perceived the global motion. If you said “yes” 8 times out of 10, you would receive a score of 80%.
Can we use this score as an indication of your sensitivity to global motion?
Evaluating the simple approach
Let’s work through an example that indicates that this simple approach suffers from an important problem. Imagine two observers that are equally good in their ability to identify global motion—that is, they are equally sensitive. However:
- Observer A is cautious by nature and needs to be really sure that they have seen the global motion before they will say “yes”.
- Observer B is confident by nature and will readily say “yes” whenever they suspect that they might have seen global motion.
When we run the experiment, we find that Observer A obtained a score of 40% and Observer B obtained a score of 90%.
This is a problem! Remember that we had defined our two observers as having identical sensitivities to global motion. If we simply took such scores as a measure of sensitivity, it would lead us to wrongly conclude that Observer B, the confident observer, had a much higher capacity for processing motion than Observer A. From the other perspective, we would wrongly conclude that Observer A, the cautious observer, had highly impaired motion sensitivity.
The main problem with this simple approach should now be clear — it confounds an observer’s sensitivity with their willingness to say “yes”. We refer to this willingness as the observer’s bias.
A framework for perceptual decisions
Clearly, we need a way to disentangle the sensitivity of an observer from their bias — this is where signal detection theory can be applied.
First, let’s introduce signal detection theory by working through its interpretation of the ‘simple approach’.
On each trial, the presentation of the “signal” stimulus will evoke some sort of internal response in the observer. For example, when you viewed the 100% coherence rightwards global motion stimulus, that physical stimulation would have affected your sensory system in some way. We summarise this effect by putting a number on it. What does this number mean? For now, it is sufficient to think of this ‘internal response’ number as corresponding to how much your sensory system is affected by the physical stimulation. A stimulus that greatly affects your sensory system will evoke a larger ‘internal response’ than a stimulus that only weakly affects your sensory system.
For a ‘real-world’ example of perceptual decision making, we will consider refereeing in sport.
Many sports require the referee to make perceptual decisions. In each case, we can think of the decision-making scenario in terms of the likely magnitude of ‘internal response’:
- A tennis linesperson judging whether the ball was ‘out’ (none of the ball touching the boundary line). A ball that is ‘out’ by a wide margin would evoke a high level of ‘internal response’, whereas one that is very close to the line would evoke a low level.
- A cricket umpire deciding if the ball touched the bat on the way through to the wicketkeeper. A very clear deviation in the trajectory of the ball would evoke a high level of ‘internal response’, while a tiny nick off the bat would evoke a low level.
- A soccer linesperson judging whether a player is ‘offside’. An attacker who is well past the last defender (other than the goalkeeper) would evoke a high level of ‘internal response’, while an attacker who is close to being in line with the last defender would evoke a low level.
- An AFL umpire deciding if the ball has crossed the goal line after being touched by a defender. A defender touching the ball well after it has passed the goal line would evoke a high level of ‘internal response’, while a defender touching the ball while it overlaps with the goal line would evoke a low level.
- A rugby league referee judging whether a player has scored a ‘try’ by putting the ball down in the in-goal area. A player planting the ball on the ground would evoke a high level of ‘internal response’, while a player who just grazes the grass with the ball would evoke a low level.
The last example, of referee decision making in rugby league, is particularly interesting for reasons that will be expanded on below.
Can you think of other ‘real-world’ examples?
Across many trials, the effect of the same physical stimulus forms a distribution of ‘internal response’ magnitudes. We typically assume that this is a normal distribution with a particular mean and variance. An example of such a distribution is shown in the interactive figure below. This figure tells us the probability of a stimulus presentation generating an internal response of a given magnitude. By moving the ‘Signal mean’ slider in the interactive figure, you are changing the magnitude of the mean internal response to the stimulus.
Given what you know about global motion and coherence from the previous section, what do you think is likely to happen to the ‘Signal mean’ in reponse to stimuli of increasing coherence?
With increasing coherence, there is more ‘signal’ present in the physical stimulus. We would thus expect the magnitude of the internal response evoked by a stimulus (the ‘Signal mean’) to increase with increasing coherence.
As discussed, the ‘internal response’ is typically conceived as an abstract dimension that captures the relevant aspects of the organism’s response to the stimulus. You could think of it as being proportional to the firing rate of a set of neurons in the brain. Though hugely simplified, this relationship may not be far from reality in certain situations—such as the processing of coherent motion (see the study by Britten et al. in the Additional resources).
We will consider this further in the upcoming Mechanisms for sensitivity section.
So, we assume that the presentation of a stimulus evokes a particular magnitude of internal response in the observer. However, the observer now needs to interpret this response in order to produce their decision — whether to respond “yes” or “no” on a particular trial.
Signal detection theory proposes that observers use an internal ‘yardstick’ called a criterion to produce their judgements. The theory says that if a given stimulus presentation generates an internal response that is greater than the criterion, the observer responds “yes”. If it generates an internal response that is less than the criterion, the observer responds “no”.
If we know the distribution of internal responses produced by a stimulus and we know the observer’s criterion, then we can specify the proportion of presentations that we would expect an observer to respond “yes” — as shown in the interactive figure below. Informally, we can look at how much ‘blue’ there is to the right of the criterion in the figure below.
For example, if the criterion is positioned at the same point as the “Signal mean” then the observer would be expected to respond “yes” 50% of the time and “no” 50% of the time.
Where would cautious and confident observers position their criterion?
A cautious observer requires a large magnitude of internal response to respond “yes”. Hence, they would have a high criterion.
A confident observer only requires a small magnitude of internal response to respond “yes”. Hence, they would have a low criterion.
We discussed above the scenario in which a rugby league referee needs to make a decision about whether a player has touched the ball to the ground or not.
However, the referee also has the option of passing the responsibility for the decision onto a ‘video referee’, who can view replays of the incident and can view also potentially view it from multiple camera angles.
Interestingly, the on-field referee is still required to make a decision and to communicate this decision to the video referee. That is, they need to tell the video referee whether they think it is a try or not a try.
How would you expect this information to affect the video referee’s criterion?
This can produce the situation in which the same physical stimulation could be ruled by the video referee as a ‘try’ or a ‘no-try’ depending on whether the on-field referee ruled that they thought it was a try or not. While this situation is often controversial for fans, it makes sense when viewed through a signal detection theory framework — in which perceptual yes/no decisions are inevitably a combination of physical stimulation and decision criterion.
A similar strategy is also adopted in cricket and AFL, in which the on-field umpire is required to make a decision prior to a video review. Interestingly, it does not happen in soccer (for goal-line decisions) or tennis — the linesperson’s decision does not influence the decision based on the electronic line judge.
How does that help us?
So far, we have used signal detection theory to understand the problem that we had with our ‘simple approach’. We have seen that the proportion of times an observer responds “yes” depends on both the magnitude of internal response that a stimulus evoked (their sensitivity) and the location of their criterion (their bias).
Considered another way, a certain proportion of “yes” responses could be generated from multiple combinations of sensitivity and bias. For example, if an observer’s signal mean is 1.0 and their criterion is 2.0, then they would be predicted to respond “yes” on approximately 16% of trials. However, the observer would also be predicted to respond “yes” on 16% of trials if their signal mean was 0.5 and their criterion was 1.5.
Can we now use the framework provided by signal detection theory to circumvent the problem that we have identified?
The key insight from signal detection theory is to also present the observer with situations in which the aspect of the stimulus that is being judged is not present. This is called a ‘noise’ trial, in contrast to the previous situation which is termed a ‘signal’ trial. For our example situation, global motion sensitivity, an appropriate ‘noise’ trial would involve the presentation of a dot motion stimulus with 0% coherence. We assume that the presentation of this stimulus will evoke an ‘internal response’ centred around 0.
By presenting the ‘noise’ and ‘signal’ trials in random order, the observer does not know beforehand whether a given trial contains the signal — all they have to go on is the magnitude of their internal response. It follows that there is likely to be a certain proportion of ‘noise’ trials in which the observer says “yes” — and this proportion tells us about the location of the observer’s criterion.
For example, use the sliders below to examine the effect of changing sensitivity and criterion on the proportion of times an observer is predicted to say “yes” to trials in which the signal is present (signal) and “yes” to trials in which the signal is absent (noise).
How does this help with disentangling sensitivity and bias?
The previous example showed that we could not distinguish an observer with a signal mean of 1.0 and criterion of 2.0 from an observer with a signal mean of 0.5 and a criterion of 1.5.
Explain how the inclusion of the ‘noise’ trials now allows these two observers to be distinguished.
As shown previously, both observers would be predicted to respond “yes” on approximately 16% of the ‘signal’ trials. However, they are expected to respond differently on the ‘noise’ trials — the observer with the lower criterion (0.5) would be expected to respond “yes” on approximately 7% of ‘noise’ trials whereas the observer with the higher criterion (2.0) would be expected to respond “yes” on approximately 2% of ‘noise’ trials.
We will look more into how this works in the subsequent sections.
A simple approach of measuring perception, in which a stimulus is presented and the observer is required to answer “yes” or “no” regarding the perception of some aspect of the stimulus, confounds the observer’s sensitivity to the stimulus with their willingness to respond “yes” (their bias). Signal detection theory provides a framework for teasing apart sensitivity and bias — by including trials in which the stimulus property of interest is not present (‘noise’ trials), we can distinguish an observer’s sensitivity from any bias they have in their willingness to respond “yes” or “no”.