Example
We will now do an example 'experiment' to see signal detection theory in action.
A demonstration experiment
To prepare, you will need a way to indicate your response ("yes" or "no") to each trial. You could write your responses down on a piece of paper, or open a text editing program on your computer. There will be a total of 60 trials for which you will need to record your "yes" or "no" response. Start by making a list of numbers from 1 to 60 on whatever method you have chosen to record your responses.
The video below will show the 60 trials sequentially. After you have watched each stimulus (moving dots), record whether you thought that a proportion of the dots moving in a common direction (rightwards) as "yes". If you thought they were all moving randomly, record "no". Make your recording next to the appropriate trial number (1 to 60).
This procedure should take around 3-4 minutes.
The trials will proceed quite quickly! Don't spend too long deliberating on each trial, or rewind and watch a trial again — simply note down a Y or an N (or some other way of indicating "yes" or "no" that you can decipher).
When you're ready, Left-click on the play icon (▶) in the video below and record your responses as the video progresses.
Congratulations, you have just participated in a psychophysics task!
Summarising your data
Let's now work through the process of determining your sensitivity.
The first step is to sort your responses into those for 'noise' and for 'signal' trials. There were actually three different coherence levels in the demonstration (in addition to 0% coherence 'noise' trials), but here we will begin by only looking at the middle coherence level.
To begin, create a table like shown below:
| No | Yes | ||
|---|---|---|---|
| Noise | |||
| Signal | |||
The rows in this table break down the set of trials into those where there was only noise and where there was signal, and the columns break down the trials according to whether you responded no or yes. We can classify these combinations as follows:
| No | Yes | ||
|---|---|---|---|
| Noise | Correct rejection | False alarm | |
| Signal | Miss | Hit | |
The terms here are defined as:
- Correct rejection
- The stimulus contained only noise, and the observer responded "no".
- Miss
- The stimulus contained signal, but the observer responded "no".
- False alarm
- The stimulus contained only noise, but the observer responded "yes".
- Hit
- The stimulus contained signal, and the observer responded "yes".
Now, fill in this table with your responses to the trials in the video. To do so, you will need to know which trials were noise and which were signal and noise. Here are the relevant trial numbers:
- Noise: 5, 19, 26, 27, 30, 31, 43, 48, 49, 50, 52, 53, 55, 56, 57
- Signal: 2, 13, 14, 16, 18, 20, 24, 33, 35, 36, 37, 38, 39, 46, 60
To fill in the 'Correct rejection' cell, count the number of "no" responses you made for the Noise trials listed above. Similarly, count the number of "yes" responses to made for the Noise trials listed above to fill in the 'False alarm' cell. Use the same process to fill in the 'Miss' and 'Hit' cells for the Signal trials.
If you find that the count in your hit cell is 15, your performance was at ceiling and we should use your responses from the more difficult trials. Repeat the process above with the following trial numbers for the 'signal' trials:
- Signal: 1, 6, 8, 10, 12, 15, 17, 23, 25, 29, 34, 41, 42, 45, 54
However, if you find that the counts in the 'Hit' and 'False alarm' cells are roughly equal, we should use your responses from the easier trials. Repeat the process above with the following trial numbers for the 'signal' trials:
- Signal: 3, 4, 7, 9, 11, 21, 22, 28, 32, 40, 44, 47, 51, 58, 59
Here is an example response table:
| No | Yes | ||
|---|---|---|---|
| Noise | 10 | 5 | |
| Signal | 6 | 9 | |
To check your numbers, you can sum across rows and columns as in the below. The number of Noise and Signal trials should each equal 15. The number of "no" and "yes" responses may vary.
| No | Yes | ||
|---|---|---|---|
| Noise | 10 | 5 | 15 |
| Signal | 6 | 9 | 15 |
| 16 | 14 |
The final step in summarising the data is to convert the counts into proportions (rates). To do so, divide the number of "no" and "yes" responses by the number of trials in their corresponding row. This is essentially saying, for correct rejections, "When there was only noise present, on what proportion of trials did the observer respond 'no'?".
| No | Yes | ||
|---|---|---|---|
| Noise | 0.67 | 0.33 | 1.00 |
| Signal | 0.40 | 0.60 | 1.00 |
| 1.07 | 0.93 |
What do the "hit" and "false alarm" rates refer to?
_
We have now summarised our data in a way that we can interpret in the framework of signal detection theory.
Interim summary
In a yes/no task, the observer is presented with a series of 'noise' and 'signal' trials in random order. The number of responses in each of these four conditions ('noise' "no"; 'noise' "yes"; 'signal' "no"; 'signal' "yes") are tabulated to produce estimates of the rates of correct rejections, misses, false alarms, and hits.
Calculating sensitivity
You have now quantified your performance on the coherent motion task in terms of your miss, correct rejection, hit, and false alarm rates. Because the miss and correct rejection rates are complementary to the false alarm and hit rates respectively (i.e. the miss rate is one minus the hit rate and the correct rejection rate is one minus the false alarm rate), we can just concentrate on the hit and false alarm rates without any loss of information.
As a reminder, the hit rate captures the probability of responding "yes" when the signal was present, whereas the false alarm rate captures the probability of responding "yes" when there was no signal present.
Now, we can use your hit and false alarm rates to estimate your perceptual sensitivity on the task. The key is to position the criterion and the mean of the 'signal' distribution such that they give the hit and false alarm rates that you obtained.
Start by using the 'Criterion' slider to adjust its position until the false alarm rate (the "Noise 'yes': %" value) is as close as possible to your false alarm rate.
The false alarm rate in the example table was 33%. Where should the criterion be set to produce this outcome?
_
Then, adjust the 'Signal mean' slider so that the hit rate (the "Signal 'yes': %" value) is as close as possible to your hit rate.
The hit rate in the example table was 60%. Where should the signal mean be set to produce both this outcome and the false alarm rate in the example table (33%)?
_
Once adjusted, the value of the 'Signal mean' is what is referred to as your perceptual sensitivity. This describes the distance between the centres of the distribution of internal responses produced by noise and produced by signal, and is known as d' — pronounced 'dee prime'.
The higher the d' on a given task, the higher the perceptual sensitivity. A d' of 0 is consistent with a complete lack of sensitivity to that particular visual stimulation.
Summary
With knowledge of the hit and false alarm rates, an observer's sensitivity and criterion can be estimated. The estimated sensitivity corresponds to the difference in the means of the 'noise' and 'signal' internal response distributions, and is known as d'.