Working with StatCrunch: Correlation Coefficients Video Lecture | Statcrunch Tutorials for Beginners - Data & Analytics

Hi, my name is Bart Poulson and in this tutorial
I'm going to show how to use StatCrunch to,
uh, create correlation coefficient. It's a
good way to analyze the relationship between
two quantitative variables. Actually, it's
a very flexible approach. You can even use
it with, uh, dichotomous categorical variables
or ordinal variables. If those come up, I'll
show you. But first I wanna show simply how
to get correlation coefficient and a correlation
matrix. The first thing to do, of course,
is to go statcrunch.com and to log into your
account over here. Um, I'm going to use a
sample data set that's already in StatCrunch.
I'm going to use one that has, uh, data about
SAT scores. And I'm going to come over here.
I want to--by the way I want to "Explore,"
"Data" so I can get to the data sets that
are online. Then come over to "Browse all"
and I'm gonna use one that's called "yms Table
1.15." Because I used it already, it popped
up as soon as I entered the first letter.
And it's this one right here with the picture
of the high school. So I'm gonna open that
up and the data set has, uh, one row for each
state in the United States with the state;
the population; average SAT verbal and math
scores; percentage of students taking it;
uh, with no--percent of people with no high
school diploma; teacher pay in thousands of
dollars--I can drag this one a little wider;
uh, the region of the country; the percent
of people over 65. Great. Um, what I'm going
to do now is I'm gonna look at the relationship
between population, verbal, math, uh, and
teacher pay. So, um, there's a few things
that I think I do take in also. I'm gonna
go to "Statistics," to "Summary Stats," to
"Correlation." And what I can do there is
I can pick my, uh, variables. I'm gonna put
the SAT ones first. I'm going to put verbal
and math—by the way I'm holding down—on
my Apple I'm holding down the Apple-key, you
know, you would use the Control-key on a PC
to select more than one of these. I'm going
to look at population, the percent taking,
and I will also look at teacher pay. So I've
selected a few variables. Um, I'm going to
ignore a selection statement where I say like
"only people over 65" or something like that
or, uh, creating different charts, you can
ignore that. I am however, gonna go to "Next"
where it says, "Display two-sided P-value
from significance test." This is an important
thing for determining whether the correlation
coefficient is reliably different from zero,
so I always select that. And then I just press
"Calculate." And here's what we've got. Let
me just make this table a little larger. OK.
What I have are the variables listed, uh,
down the side and across the top. SAT math
is here and here. Population's here and there.
Taking is here and there and teacher pay.
Um, now this first number up top here is the,
uh, correlation coefficient for two quantitative
variables. It's full name is the Pearson Product
Moment Correlation Coefficient. Uh, different
versions of it go by different names, but
they're all calculated and interpreted the
same way. The correlation coefficient is the
number that goes from 0 which means no linear
relationship between two variables to 1 which
indicates a perfect linear relationship. It
can also be positive or negative, uh, although
that has nothing to do with the strength of
the relationship. Instead it simply has to
do with whether it's an uphill or downhill
relationship. So, for instance, uh, education
and income. The higher the level of education,
the greater your expected income. Fine. Uh,
the greater your levels of social support,
the lower your levels of stress. That'd be
a negative association. Anyhow, um, those
are the first numbers. They—so, right
here, for instance, we see that SAT math and
verbal have an outstandingly high correlation.
It's .96. That's just about as high as you
can possibly get. Remember it's 0 to 1. Um,
and it's positive, which we expect. This one
right here is, uh, negative, uh, 305. Um,
that places with larger populations have lower
average, uh, SAT verbal scores, strangely.
Also, uh, places with lower percentages of
students taking it tend to have higher verbal
SAT scores, and I've some theories about that
one. Um, anyhow, there's several other combinations
here. The number in the parenthesis is the
probability value from the null hypothesis
significance test, and the idea here is, uh,
it starts with the assumption that the correlation
in the population is zero. And then if we
have a correlation in our sample data that
is something other than zero, then it could
be due to just random fluctuation-fluky chance.
And this says, "What is the probability of
getting a correlation this big or larger through
random sampling error if the true correlation
is zero?" And what you're looking for here
is a number that is small, meaning less than
.05. So, for instance, is one right here is
0.0293. That's less than 05. And so we would
say that that correlation is statistically
significant. On the other hand, the one right
next to it between population and SAT math,
the p—the probability value is point
z—0.1817. It's greater than 05, and
so we normally would not consider this statistically
significant. On the other--it's pretty easy
to see because the correlation coefficients
vary in the opposite direction. So, a bigger
correlation coefficient here, the 30, has
a lower P-value, the 29, 029, Whereas the
smaller correlation coefficient has a larger
P-value. And you can see that pattern through
the other ones. Anyhow, this is a good way
to get started looking at the relationship
between a bunch of variables. Typically quantitative
variables, but as I said, it also does work
with ordinal which means first, second, third
variables, as well as dichotomous variables
and they're especially easy to interpret if
they're down in 0, 1 variables. Anyhow, that's
that, uh, for now.