# 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.

Note

The trials will proceed quite quickly! Don’t spend too long deliberating on each trial — 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, press `Play` on 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
• 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.

• 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.

Note

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 Signal 0.4 0.6

We have now summarised our data in a way that we can interpret in the framework of signal detection theory.

### 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 below to adjust its position until the false alarm rate (the “Noise ‘yes’: %” value) is as close as possible to your false alarm rate. For example, for the demonstration false alarm rate from the previous section (0.33), I would move the criterion so that it is positioned at 0.45. This is because when the criterion is 0.45, the predicted proportion of “yes” responses to ‘noise’ trials is 32.6% — close to the observed false alarm rate of 33%.

Then, adjust the ‘Signal mean’ slider so that the hit rate (the “Signal ‘yes’: %” value) is as close as possible to your hit rate. For example, for the demonstration hit rate from the previous section (0.6), I would move the signal mean so that it has a value of 0.7. This is because when the signal mean is 0.7, the predicted proportion of “yes” responses to ‘signal’ trials is 59.9% — close to the observed hit rate of 60%.

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.

Activity

The blue ‘Note’ box above specifies the ‘signal’ trials for the other two coherence levels. Use that information to calculate your sensitivities for each of the three coherence levels.

What happens to your sensitivity as the coherence increases?

### 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’.