Instructor: Hello students, this is problem 2e.
And this actually is not in our text,
but it has been added because we want to show you guys
how to determine if two factors are independent or not.
So we are continuing to use the same example,
and we want to know now
if the child's hyperlipidemic status
is independent of the parent's status.
So conceptually, this means that the probability
that the child is hyperlipidemic should be the same
regardless of the parent's hyperlipidemia status,
and that will demonstrate independence.
So mathematically, what we want to do here is
look at this probability,
and I'm going to start.
And again, here I am abbreviating hyperlipidemia as HL,
and we are going to use
the both parents being hyperlipidemic,
but we could use the other columns as well.
Okay, let me write a little smaller,
so that they will fit here.
So now, what are these numbers?
So for this one,
and we have gone through this calculation before,
the numerator is going to be 45 plus 42 plus six
because again, the child's hyperlipidemia status
was given in the rows and the parents in the column.
And then we are going to divide this by 223,
which is our entire cohort.
On this side,
it's going to be 45 divided by 45 plus 13.
Again, I like to put the parentheses around
because it helps me remember
that I have to do the addition before I do the division.
So now what I'm gonna do is go and get a different color,
so I can show you where each of these are coming from.
So this is where we are getting
the child status from, right.
Okay, this row,
and that's exactly what we have there.
And then this is our denominator
for the left hand side.
And now, for the right hand side,
I'm going to show you where 45 is coming from.
Of course, it's coming from here,
and the parent status is coming from here, okay.
So,
this is basically what is going on,
and this is how we are doing our calculation.
So now, let's go back,
let me get the black ink,
and I'm going to start doing the calculation.
And when we do the calculation what we see is
from this side, we get 0.42,
and from this side, what we get is 0.78.
So what?
0.78, so basically we can say that they are not equal.
So since they are not equal,
now we can say that they are not independent.
So not equal here means
not independent.
Let me see if I can write this a little more nicely.
So not equal,
not independent.
Okay.