So for any certain task, what we're going to have is a noise threshold. So we're going to have a noise distribution. And the noise distribution might kind of look something like this.
So this is just background noise. So what this basically shows is if we were to take a bunch of individuals and we showed them a bunch of, we experimentally tested signal detection theory, you would get this graph just kind of indicating the noise. And then we'd get a second graph, which is kind of shifted over to the right a little bit, and this is the signal distribution. So this is the signal distribution, and in the blue over here we have the noise distribution.
So the difference between the means of these two distributions is d prime. So if the signal distribution was shifted over here to the right, then d prime would be really big, it would be a really easy task, it would be something kind of like this. whether there's a green dot on the screen or not. But on the other hand, if the signal distribution was shifted over to the left, then D prime would be super small and it'd be something more like this, like a more difficult task.
So the x-axis here, we have the intensity of the stimulus, so that would be how easy the stimulus is to distinguish from the background. Okay, so we've got the first variable, which is D prime, and the second variable is C, and that is the strategy of the individual. So strategy can actually be, strategy can be expressed via the choice of the threshold.
So what does the individual deem as necessary? What threshold is necessary to surpass in order for them to say yes versus no? So we're just going to label the different strategies.
So there's B, there's D, there's C, and there's beta. So these are different strategies, and they're just variables given to the different strategies. So if we were to use this.
B strategy, this would basically say, okay, I'm going to choose a certain threshold. So let's say that I choose this threshold over here. So let's say that I choose two. So anything that is greater than two, I will say yes to.
And anything that's less than two, I will say no to. So in that case, the probability of a hit is this area over here. And the probability of a false alarm is this area over here. So that would be the B strategy.
The D strategy basically says, okay, so the position of my threshold is going to be relative to the signal distribution. So basically what that comes out to be is D prime. So the signal distribution, if it's over to the right, we'll have a big D prime.
So D prime minus B. So we choose a threshold, let's say two, and let's say that D prime in this example is one. Then we would have two minus one. and we'd get one.
So if we were using the D strategy, then anything above a one would get a yes, anything below would get a no. So the C strategy would be an ideal observer. So this would be someone that would be minimizing the possibility of a miss and of a false alarm.
So the C strategy is basically, if we were to write an equation for it, it would be B minus D prime over two. So in our example it would be 2 minus 1 divided by 2, so that is equal to 1.5. So if you were using a C strategy, that of an ideal observer, then we would say anything above 1.5 would get a yes, anything below would get a no. And so we said over here that the C, this C variable is indicative of the strategy that a person uses.
So when C equals 0, then the participant is an ideal observer. If c is less than one, we say that the participant is liberal. And if c is greater than one, we say the participant is conservative in their strategy. And this would be ideal.
So when we say conservative, that means that they respond no more often than an ideal observer. And when we say liberal, then that means that the participant says no less often than the ideal observer. So the final Variable that we have to talk about is beta so if we're using this beta approach We would set the value of the threshold equal to the ratio of the height of the signal distribution to the height of the noise distribution and so it's easier to actually look at beta in This way so if we were actually writing the equation we would say the natural log of beta is equal to D prime times C And so in this case, it would equal 1 times 1.5, which equals 1.5.