So now let's look at moderation.

And we'll look at first the model and then the graphical example of moderation.

So moderation is a different statistical test.

And what it says is, or what it tests is, that the relationship

between variables X and Y is predicted by the value or level of M.

So, the model is different here.

I'm modeling y, and regressing y on X, M and the X*M interaction.

Usually those are centered before hand as well.

So in a linear modeling framework you can see this here.

So I've got y is Beta naught + Beta1 timex x + Beta2 times m + d,

which I'm calling the moderation effect there, times the (x*m) interaction.

And that d tests the moderation effect.

So mediation and moderation are distinct statistical tests.

But in some cases we might expect both.

So for example, if X really drives increases in M and Y and when X is off,

like the hose in a water pipe is off, there's no flow,

then there's really not much happening in either M or Y.

And in such a case, we would expect both mediation and

moderation to be significant.

So here's a graphical example of moderation now.

And this is a great example, in keeping with our theme.

So now what we're looking at in this study is

whether the correlation in opioid binding values between the inter singular and

the PAG in the mid brain, both opioid rich areas, is stronger

when you're on a placebo versus no placebo or just a control condition.

And this is what we'd expect

if there's a widespread increase across the brain in opioids with a placebo

that causes those areas to become more correlated with one another.