Knowledge by Association. We often hear people tell us things about
associations between two variables. In so doing, they seem to be telling us
something really profound, or something important.
let me give you a surprising one that I heard once and it really had me
scratching my head. I heard on the radio that, the more
cheeseburgers that one eats, the lower the rate of dying of cancer.
What? Eating cheeseburgers protects you from
death of cancer, by cancer? It turns out it's true.
And that sounds really impor, informative, right?
It might make you think wow, I have to change my diet.
I should go out there and start eating a buncha cheeseburgers.
Now, as a vegetarian saying this to you, I have to tell you that's a very hard
thing for me to say. But in fact, it's not the right course of
action, either, because the reason that correlation exists is because eating a
lot of cheeseburgers, increases by a significant amount your likelihood of
dying of a heart attack. If you die of a heart attack, you can't
die of cancer. So these things can be very tricky.
Yeah, it's not, it's not, eating cheeseburgers is not reducing your
likelihood of dying; you just die of a heart attack before you can die of
cancer. So, you really shouldn't go an eat a
bunch of cheeseburgers. Veggie burgers, maybe, not cheese
burgers. this is the trick with, with association.
So lets consider association in detail because there is a lot of value in these
studies, but its just important that the consumer of this information understands
the limits. So let's do it.
Week one, Lecture seven, knowledge by association.
I want to start by just giving you a real concrete feel of this.
And, and this is one of, a really cool study in psychology that gets a lot of
people's head kind of scratching like, what is this about?
And it's all about marshmallows, and you would never understand the power that a
marshmallow could have as a diagnostic instrument.
But it turns out it does. So what I'd like you to do before I talk
any more, is check out each of these links in succession.
So first of all, click on the Stanford marshmallow experiment link, watch the
video about that and then check out the article about it that appeared in The New
Yorker. And think about all of that stuff and
then come on back. Okay?
Cool. All right.
Welcome back. Pretty cool, eh?
Wow. Just, you know, being able to wait to
what's called delay gratification, those who could delay gratification longer,
seem to have more success in life, measured all sorts of ways, including
something as concrete as an SAT score. What does that study tell you?
I mean, it's cool, it's fascinating. Does it give you answers?
Or does it raise questions? In my opinion, it raises more questions
than it does answers. And the answers it gives you are really
kind of tenuous. I mean, it does tell you, well there's
something there, there's some sort of link.
There, there's a good reason to investigation this relationship further
but it kind of stops there. All right, let me hold that point for a
moment, because we, we're going to have to spend a little bit of time getting you
used to some of the terminology people use when they talk about correlations.
And some of the graphical depictions they use.
So specifically, these things are things called scatter plots, so this is six
different scatter plots. Each one of these scatter plots shows you
a correlation coefficient within it, that thing that says r.
So, I want to make these make sense for you, so let's go to a different example
for now, an example I've kind of depicted over here.
Imagine we asked a bunch of women to rate two things about themselves.
the first is just their height. Tell us how tall you are.
The second is on let's say a 1 to 10 scale, how attractive do you feel?
How attractive of a woman do you think you are?
And we want to know if there's a relationship between this, between height
and attractiveness. But here's the twist.
Let's say we ask 18 year old women this question, but we also asked 13 year old
women this question. Why 13?
Let me get to that. Let's start with the 18 year olds.
What would we expect for 18 year old women?
Well, our society seems to value tallness for some reason.
We tend to associate tall people as being more attractive.
And so what we might expect is that the taller women, will consider themselves
more attractive. So, on this scatter plot, each one of
these points represents a single person, and it represents two things about that
person. How tall were they?
You could figure that out by following this down to here.
That tells you how tall they were. And how attractive did they feel they
were? You figure that out.
By going over here. So, this is somebody that's sort of
shortish you, know short to medium and doesn't think they're very attractive.
Where as this person relatively tall and does think they're attractive.
this other person by the way is actually a little shorter than the one I was just
telling you about. Just a smidge shorter but they really
think they're attractive. Okay.
So every one of these points is just that, a single person.
And when we now lay these points out, we can get a sense of the shape of what's
sometimes called the cloud. Lemme give you a sense of that.
That's okay. You can kind of see it with your eyes if
I just trace my mouse like this. This is like the cloud of points, and we
want to know a couple of things about this cloud.
We want to know which direction it goes. Does it go like this one, which is, sort
of, up into the right. When something goes up into the right
like that, as this line kind of shows you.
That's what we call a positive correlation.
That means these two variables have a very specific kind of relationship.
As one variable gets bigger, the other one also tends to get bigger.
OK? They go together.
They're positively related, so the taller somebody is, the more physcially
attractive they feel. Both of those things kind of grow
together or shrink together. The shorter somebody is, the less
physically attractive they feel. Okay, that's what we call a positive
correlation when that's true. this number represents how strong that
correlation is and it can range from zero to one.
