In this video, I'm gonna show you how to calculate correlations in SPSS. I'll focus on Pearson's
r, although the process will be pretty similar for other types of correlations correlation
coefficients. So just a quick review on on Pearson's r, it describes the relationship
between two continuous variables, it ranges between negative one and positive one, where
negative one means a perfect inverse relationship, zero indicates no relationship at all, and
positive one indicates a perfect direct relationship. Anything between zero and one, or zero and
negative one, indicates varying strengths of relationship. So let's pretend we're interested
in the relationship between IQ and GPA. So first let's get some data in here, which I'm
just gonna paste in from some numbers I made up earlier. You can pause the video now and
enter them in. So as you can probably guess, this first column are IQ scores, they range
from about the 80s to around 120. The second column indicates different GPA scores, which
have the potential to range between zero, which means you're failing everything, and
4.0 means you're acing everything. And it looks like in this dataset the lowest score
is about 0.8 and the highest GPA is about 3.7. So before we do anything else, let's
make this easy on ourselves and rename these variables. So I'm gonna go over to variable
view, and just rename this first one IQ scores, and the second one GPA. And I think all the
other default settings can stay the same. So these data are set up in a very specific
way. The order of the scores really doesn't matter as long as each pair stays together.
So for example, this first person has an IQ of 112 and a GPA of 3.3. And this pair of
scores can go anywhere, it can go at the top, it can go somewhere towards the bottom or
it can go in even the middle. The point is, they need to stay together. And indeed these
scores I have in here aren't ordered in any logical manner, the only thing that's important
is that each IQ score stays with each GPA, cause it reflects scores obtained from one
individual person. This is one person's IQ and GPA, this is another person's IQ and GPA,
some third person's IQ and GPA. If we change the order of one set of scores, but leave
the others the same, our correlation coefficient won't reflect reality, because it'll be mismatching
scores from different people. So just remember that data from each person must be paired
together. Also you can see there are fifteen pairs of scores. We don't talk about there
being thirty different data points, because when we're doing correlations, it's all about
how many different pairs of scores you have. So now that we have the data in here, it'll
be relatively easy to start on the correlation. All we do is we go up to analyze, and under
the correlate option, there are different types of correlations we can calculate but
Pearson's r is a type of bivariate, so we go there. And once we're there we see this
window that we've dealt with before. All the variables we have are on the left, everything
we wanna analyze we move over to the right. So in this case we need to move over at least
two variables, if I move over just one it won't let me run the analysis, OK is not available.
Because if we only had one variable, what would we compare to? So we need to have at
least two things. We have some different options here too, there are different types of correlation
coefficients you can calculate, Pearson's r is one of the most widely used ones, so
it's already checked right here. And it's also the most appropriate for these data,
there are also ones like Kendall's Tau or Spearman's Rho. We could use those for different
types of data, for now let's just stick with Pearson's. And below, SSPS also wants to know
if we are going to run a two-tailed or a one-tailed significance test, and whether to flag significant
correlations. I haven't talked about significance tests very much yet, but these options deal
with detecting whether are correlation coefficients are significantly different from zero. In
other words, would we expect to see similar results in the real world? And I'll talk about
that more in just a minute. For now, you can just leave those options where they are. So
once you're ready, just click OK and your output window will pop up. Now what it's showing
us is in a correlation matrix, that's this box right here. This shows the correlation
coefficient of every combination of variables. So we have these two rows, one for IQ, one
for GPA, and we have two columns, one for IQ, one for GPA. So where each row and column
meet, we see the correlation coefficient between these two variables. We can also see--the
correlation coefficient's the first thing--then we see the significance level, or P value,
and then the N, which is the number of pairs of scores each correlation coefficient is
based on. And remember from earlier we have fifteen pairs of scores. So in this first
square in this matrix, we see the correlation coefficient between IQ and itself. No big
surprise, it's one, it's a perfect correlation. We see another perfect correlation down here
in the lower right, which is the correlation between GPA and itself. You'll see these ones
in every correlation matrix you run, because like I said earlier, SPSS will compare every
combination of variables, including each variable and itself. So just be aware that all the
comparisons will be the same on both sides of this diagonal of ones. The comparison that
we're probably most interested in is the correlation between IQ and GPA. And notice down here,
this is the same thing as the correlation between GPA and IQ. It doesn't matter which
one you do against the other, the order doesn't matter. So first it's showing us the correlation
is very high, it's .986, or almost, almost one. Below that we also have the significance
level or p-value, which is very small. It's definitely less than .05 or .01, which are
typical cutoffs. I'll explain p-values more in a later video, but for now just know that
anything smaller than .05 means the correlation is significant, so we'd probably see it in
the real world. And this correlation was so small that we can't even see it with three
decimal places. It's probably something like .00001. And in this case the correlation has
been flagged with two asterisks, which means it's significant to the level of less than
.01, which is why it says that down here. And one last thing I wanna mention is that
we can compare more than two variables in our matrix. We can actually do a lot more,
we just need to toss in more variables in the mix. So getting back to the spreadsheet,
I've magically included some data on people's shoe sizes. So this first person, with an
IQ of 112, and a GPA of 3.30, also happens to have a shoe size of eight. So what we can
do is, if we go back to analyze, and under correlate bivariate, we can toss in these
data on shoe sizes into the mix, into our correlation matrix. So what we get when we
hit OK is, right below, we get an even bigger correlation matrix, one with three rows and
three columns. So what it's telling us is that the correlation between shoe size and
IQ is is .04. The correlation between shoe size and GPA is .06. In other words they're
both very very small. In other words, there's no relationship between shoe size and these
other things. And just for the record to you can also see these same coefficients up here,
between IQ and shoe size, there's the correlation coefficient between GPA and shoe size, there's
the correlation coefficient right there. So those are the basics of correlations in SPSS,
just remember that you can make your correlation matrix as big as you want, but they're easier
to read if you keep them small, so try and limit your comparisons of things that you
think would be theoretically interesting. Also, don't confuse correlation coefficients
with p-values, or the significance level. Remember that you want the correlation coefficient
to be big, close to one, and you want the p-value to be small, hopefully less than .05.