In this video we'll take a look at how
to calculate a correlation matrix in
SPSS. And a correlation matrix involves
calculating all possible pairs of
correlations. So, in this example here,
notice there's 3 variables. For our
correlation matrix, we'll calculate a
correlation between SAT and social
support, SAT and college GPA, and then
finally social support and college GPA.
And the way to do that is we want to go
to Analyze and then Correlate and then
select Bivariate.
Now here we want to move our 3
variables over to the Variables box. We'll
leave the default option, Pearson,
selected, since we want the Pearson r
correlation coefficient. We'll leave a
two-tailed test selected as our default
and then we'll go ahead and let SPSS
flag the significant correlations. And
we'll go ahead and test these
correlations using an alpha of .05. Go
ahead and click OK. And then here we get
the output of our correlation matrix. And,
as you can see here we have all of our
variables SAT, social support, I'll go ahead and
expand that a little bit, and college GPA
in the columns then we have the same
variables in the rows again. And where
two variables meet or intersect, that's
the bivariate correlation. Notice here on
this main diagonal, we call it, these are
all 1.0, or perfect correlations.
Well that really shouldn't be surprising
if you think about it, because this is
the correlation of a variable with
itself. So SAT with SAT, that's always
going to be 1.0, social support with
social support is 1, and college GPA
with college GPA is 1. So these are
always 1 on the main diagonal. What we
want to look at is the off-diagonal. So
either these 3 values right here in
this lower triangle or these 3
values up here in the upper triangle.
They're the exact same tests. So in other
words, notice here we have social support
and SAT, a correlation of .177. We
have the exact same thing right here,
SAT and social support, correlation of
.177. So we'll just go and look at
this lower triangle here. So notice that,
as I said before, the correlation between
social support and SAT is .177, college
GPA and SAT is .650, and then finally
social support and college GPA is
.408. Now notice that these two
correlations have asterisks next to them,
and that this one has two asterisks and
this one has one.
Well if we look at the p-values here for
each of these tests, which are shown
under Sig.,
we can see that in fact the correlation
between SAT and college GPA has a
p-value of, it's reported as .000.
What that really means is that it's
less than .0005 and it's
been rounded down. So this is a very
small p-value, and this p-value is
.015. Well notice that this
p-value of .000 is less than .01,
it's also less than .05. So this has
two asterisks because, notice here on
this note, 'correlation is significant at the
.01 level,' since this p-value is
less than .01, that's why we
get the two asterisks here. Now for this
correlation between social support and
college GPA, notice the p-value here is
.015. That's not less than
.01, since this is .015,
but it is less than .05. So it gets
one asterisk, because it's less than
.05, but not less than .01. Now
we were testing these at .05,
so we would say that SAT and
college GPA, and social support and
college GPA are both significant
correlations. These correlations are
significantly different than 0. And
notice they're both positive, so higher
scores on one variable are associated
with higher scores on the other variable.
Now social support and SAT is not
significant,
it had a p-value .310, and that's
definitely greater than .05, so this
correlation is not significant.
So we cannot conclude that it's
significantly different than 0.
OK, so in summary, these two correlations
are significant, and this one is not. And
the correlation matrix calculated all
these correlations at a single point in
time. Now there's no limit to the number
of variables you can calculate, you could
have moved 10 variables over and had 45
correlations in that case. So there
really is no limit all to the number of
bivariate correlations you can calculate
in your correlation matrix. Now we can
also test if this entire matrix itself
is significant.
Now here I'm not talking about bivariate
correlations, as we've done here, but this
whole matrix at once, is it significant.
And I'll do that in another video. Thanks
for watching.