SPSS for Beginners 5: Correlations - YouTube

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.