In this video we'll take a look at how to calculate the correlation coefficient
in SPSS. Now when we talk about calculating correlation what we mean
here is Pearson correlation.
While there are other correlation coefficients, by far Pearson correlation
is the most common correlation coefficient that's used and it's the one
that's included in introductory statistics texts. Sometimes there are
other correlation coefficients as well such as Spearman's Rho, but Pearson's is
the one that's focused on in nearly every text out there.
The Pearson correlation measures the degree of the linear relationship
between two variables. When we say linear what we mean is that the relationship
can be well characterized by a straight line.
So a straight line does a good job of representing the relationship. And
towards the end of this video after we run the correlation we'll create a couple
of scatter plots to give you a better idea of what we mean when we say 'well
characterized by a straight line'. Correlation ranges from negative 1.0
to positive 1.0. And Pearson correlation is given by the letter r and
as an example you might see something reported like r = .55. Notice that
this value of .55 ranges from negative 1 to positive 1
it's in that range. You should never see a correlation of 1.2, for example, above
this value and you should never see a correlation of negative 1.8, for example,
Those both would indicate mistakes.
So if you ever calculate and get an answer that's outside of this range or
you ever see someone report an answer outside of this range
something's wrong, so you should take a second look at your values.
There are 3 types of relationships I'd like to talk about with Pearson
correlation. And in this description we have two variables
the first variable is X and the second variable is Y.
So our first type of relationship is a positive relationship
and for a positive relationship or a positive correlation
that's saying the same thing higher scores on X are associated with higher
scores on Y. And what this means is there's a tendency for if an individual
has a high score on X
they're also going to tend to have a high score on Y. It's not necessarily
perfect in most cases it won't be but if you know someone's score on X it gives
you a good idea of where they are on Y.
High on X high on Y. For positive it's also true that if you have a lower score
on X you would tend to have a lower score on Y.
The second type of relationship is a negative relationship or negative
correlation.
Now here we see the opposite pattern. So here higher scores on X are associated
with lower scores on Y
and vice versa. Lower scores on X are associated with higher scores on Y.
So this is an opposite pattern higher on X goes with lower on Y, lower on X
goes with higher on Y.
Finally our last type of relationship is no relationship and that means there's
no predictable relationship between X and Y. And another way to think about it
is where here we had higher on X we had higher on Y for positive and for negative we
had higher on X with lower on Y,
well for no relationship we have if you have a low X
you're going to have some low Ys, some medium Ys, and some high Ys.
If you have a high X you're going to once again have some low Ys, medium
Ys, and high Ys.
There's no relationship; no predictable relationship between X and Y for
a correlation that exhibits no relationship at all between the two
variables.
OK with the background of correlation laid out let's go ahead and take a look
at our example. In this example we have the following two variables, hours of media
or hours media and college GPA. And what we did here in this hypothetical example
is we recorded the number of hours of media during a given week that
individuals engaged in. And media could be TV, movies, internet, and so on.
So we recorded the number of hours of media that people engaged in, in a given
week, and then we also obtained their college GPA and we want to see if
there's a relationship between these two variables as measured by Pearson's r our
correlation. And if you think about it if somebody watches a lot of media so
they're spending
let's say an inordinate amount of time watching media whatever form it may take.
That's not going to leave them probably sufficient time to attend to their
studies. And in that case if we had a lot of hours of media watched that probably
would suggest that the GPA may be lower.
Now this may or may not be the case we'll see what happens in this example.
But if that was true
high hours media, low GPA,
do you recall kind of correlation coefficient that would be? Well if we use
the generic variables X and Y here high on X low on Y so it's an opposite
pattern,
high on one low on the other, that you may recall is a negative correlation. So it
makes sense, at least theoretically speaking, that there could be a negative
correlation here. But let's go ahead and run the analysis and see what we find. To
run the correlation we go to Analyze, and then Correlate, and then Bivariate