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Using pairwise correlations to summarize the bivariate relationship between two continuous variables

in this video I’ll show you how to
describe the relationship between two
continuous variables using Paris
collection z’
correlations summarize the linear
relationship between two continuous
variables you can get correlations by
using the can’t command PW car for
pairwise correlations correlations
describe the relationship between two
continuous variables on a minus 1 to +1
scale when a correlation is negative it
means that as the value of one variable
goes up the other one goes down positive
correlations mean that as the value of
one variable goes up the other one goes
up The Closer a relationship is to 0 the
less related the two are changes in one
variable do not appear to correspond to
changes in the other it can be hard to
make correlations concrete so here’s
some real-world examples this is an
example of a strong negative
relationship it describes the
relationship between country’s birth
rates and the prevalence of
contraceptive use among the female
population of childbearing age this is a
strong negative relationship the higher
the birth rate the lower the
contraceptive use and the higher the
contraceptive use the lower the birth
rate the graph exhibits a pretty strong
looking relationship and it’s reflected
in a stronger negative correlation this
is an example of a pairwise correlation
that’s weak it’s close to zero it shows
the relationship between poverty and the
murder rate
as the graph suggests countries with
high rumored er rates can have a lot of
poverty or not much and countries with
low murder rates can have a lot of
poverty or not much this is an example
of a positive relationship with a
pairwise correlation that’s 0.82 is
close to +1 it shows the relationship
between countries GDP per capita and the
number of entry that users per hundred
people the variable is strongly
correlated really poor countries tend
not to have many Internet users and
richer ones have a lot of them we use
the PW core command to get pairwise
correlations the syntax is PW core and
then a list of variables separated by
spaces this command will get you the
pairwise correlation between three
variables GDP per capita life expectancy
and Internet users the results suggest
that there’s a reasonably strong
positive correlation between all three
variables as an economy tends to get
richer it tends to have longer lifespans
and more internet use likewise it
suggests that internet use and lifespans
are positively related there are at
least two options you can use with the
PW core command the option OBS is for
observations it asks data to report how
many observations were used in
calculating the pairwise correlation
this is useful because sometimes we
don’t realize that we’re making
inferences about correlations based on
really small sample sizes it’s always
good to run it with the OBS option once
this is an example of what it looks like
when we use the OBS option it shows that
these pairwise correlations are
calculated between 171 and 188
observations the sinc command asks data
to give the results of a significance
test
that the correlation is nonzero when you
use this command you’re looking for a
significance score that’s less than 0.05
in this case all of these relationships
score below point zero five suggesting
that they are all significant this means
that we predict there’s a high
likelihood that all of these variables
have nonzero relationships
let’s review correlations describe the
relationship between two continuous
variables to get pairwise correlations
we use the command PWR and the list of
variables that we want to have
correlated the option herbs will last
data to report the number of
observations upon which our correlation
estimates are based and sake will ask
data to perform a significance test to
determine whether or not we have good
evidence that two variables have a non
zero pairwise correlation for more
information on this command type help PW
core in the state of command window

Department of Sociology

Powdermaker 252

City University of New York, Queens College

6530 Kissena Boulevard

Queens, New York 11367

joseph.cohen@qc.cuny.edu

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Unless indicated otherwise, original textual documents on this site are distributed with a Creative Commons BY-NC-SA 4.0 license. Most images on this site are public domain (look for the Dall-E symbol in the bottom right corner), though some are original or used as Fair Use as part of my public scholarship work as a university professor working in the City University of New York system.