Voiceover: For any certain task, what we're going
to have is a noise threshold.
So, we're going to a 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,
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 is
a green dot on the screen or not.
But, on the other hand, if the signal distribution were
shifted over to the left, then d-prime would be
super small, and it'd be something more like this,
like the 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 is 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,
will 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 two minus one
divided by two, so that is equal to one point five.
So, if you were using a C strategy, that of an ideal
observer, then we would say anything above one point five
would get a yes, anything below would get a no.
And so, we said over here that the C variable is
indicative of the strategy that a person uses.
So, when C equals zero, 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 virtue, we accept 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 an equation,
we would say the natural log of
beta is equal to d-prime times C.
And so, in this case, it would equal one times
one point five, which equals one point five.