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Whenever you explore your data you'll find that each step can build on the others before it. In this course for example we started by looking at individual variables before looking at pairs of variables and that comes before looking at sets of variables. When we looked at individual variables we started by creating graphic displays for each variable. Then by computing descriptive statistics for each and finished with inferential statistics. There is a logical progression to this and it's one that we will follow here with the associations for pairs of variables and later for sets of variables.
The first procedure that we are going to look at, correlations, is the most general measure of association between pairs of variables. Let's look at how to do correlations in SPSS and how to interpret the results. For this example, I'm going to be using the same dataset I've used in the last few. It's about the Google Searches, Searches.sav, and to get correlations we need to go up to Analyze and then we come down to Correlate, and what we are going to be doing is the basic version called Bivariate or two variable correlations.
All you need to do here is take all the variables that you want to correlate with each other and put them in the variable list on the right. Now if there is one variable in particular that can serve as an outcome variable, it's helpful to put that one in first so it shows up at the very top of the list. In this particular example I thought it might be interesting to look at the relative interest in searching for Facebook. So I am going to put that in first, and then I'll see how that compares with other search terms by selecting all of these, and I might as well put in nearly everything here.
I am going to come down to Median Age, because all of these are either scale or dichotomous. Now I am not going to put in Census Bureau Region because that has four categories and Census Bureau Division because it has even more. However, you can use indicator variables and what I've done is I've created three indicator variables. One for whether a state is in the Northeast, another for the Midwest, and a third for the South, and what that does is it leaves implied in all of these is the West.
So I am going to add the three of those and put them over here. Now I have a few options with correlation. I can get three different kinds of correlations. There is the Pearson Product-Moment Correlation coefficient which is the standard correlation, also sometimes known by its symbol R. There's Kendall's Tau-b and there is the Spearman rank order correlation coefficient. Truthfully, I've never had to do with anything other than the Pearson and I recommend that you stick with that one. There's also Test of Significance.
You can do what's called a one- tailed test or a two-tailed test. Now this has to do with calculating false positive rates and I recommend that you always stay with a two-tailed test unless you have some super-compelling reason to go with the one-tailed. Also, we have the option of flagging statistically significant correlations. That's very helpful and I'd leave that on there, and let's come over here and take a quick look at the other options. You can also get means and standard deviations for each variable, but we don't need that at this point, because we should have done that already.
You can get what are called cross- product deviations and covariances and that's a little technical and we don't need that. The other question is whether you want to exclude cases pairwise or listwise. I've mentioned these before. Pairwise means that you might have a different sample size for each set of correlations. If for instance everybody has data on two particular variables, but you're missing a lot of information on another variable, you would end up with different sample sizes. This isn't necessarily a problem and I usually leave it at pairwise.
However, there may be times when you only want to deal with cases with complete information, in which case you would choose listwise. But I am going to leave it at the default for right now. So I'll press Continue and I'll press OK. Now I asked for a lot of variables and so what I get here is a very large table. You can see that it goes down a long way and it goes across a long way. You can also tell that the labels aren't there and when we scroll down it's hard to see. But that's okay, and what you see here is that every variable is listed down this side.
We have Facebook to SPSS to Regression as Google Searches, and we have the same variables listed across the top: Facebook, SPSS, Regression, and so on. Then what you have is a cell that gives information about the association between each one. In each cell the top number is the Pearson correlation. That's the actual correlation coefficient. It goes from 0 to 1 and 0 means no linear relationship and 1 indicates a perfect linear relationship. It can be positive or negative.
The positive or negative has nothing to do with the strength of the relationship. It only indicates whether it's an uphill or downhill relationship. The second number it says Sig. Two-tailed. This is the probability value that's associated with the significance test for the correlation, and the third one is the N or the number of cases that go into calculating that particular correlation. This dataset has complete data for all 51 cases. That's the 50 states in Washington, D.C. Additionally, you see that down the diagonal we have a series of 1s and blanks and 51s.
That's because it's each variable correlated with itself which will always be a perfect positive correlation, and truthfully some programs just don't put anything there at all. But let's say I'm interested in the relative interest in each state in searching for Facebook. Then what I want to do is I want to go down this first column. It says Facebook at the top and I want to scroll down and I want to look for statistically significant correlations. Now SPSS makes this easy, because they will put asterisks next to statistically significant correlations.
So you see for instance the top is Facebook correlated with itself. That doesn't really mean anything. Facebook and SPSS have a correlation of -.184. It's not a very strong correlation. It's closer to 0 than it is to + or -1 and you can tell that its probability value is .196. It's nowhere close to a statistically significant. However, we do see that in the next few we have statistically significant negative correlations. The higher a state's interest in Facebook the lower its interest in searching on Google for regression or statistically significant or business intelligence.
We can scroll down and see some more. Similarly, lower interest in data visualization, they're also less likely to use the term totally lost. On the other hand, states that show a relatively high interest in Facebook also show a relatively high interest in searching for American Idol. That's the correlation of .516 and as that probability value of 000 is not actually a 0, but it means that it rounds off to less than 001. As we scroll down we see that modern dance goes into it and NBA.
Interestingly, NFL does not correlate, but the NBA and FIFA do. Also, as we scroll down we can see that states that have an NFL team show a lower interest in Facebook, similarly for an NBA and MLS. It's just as whole series of correlations that show things that can be used to predict the level of interest in a particular item. Now the most important thing probably to remember here is that correlations are simply associations. They don't explain why the variables are associated.
It's simply a predictor. The matter of explaining why they are correlated is a whole different issue about causation and something that we need to be careful about. So in summary, correlations are great way to look at the strength of associations between two variables. The correlations of general purpose they can be used with scale variables, ordinal variables or dichotomous variables, and they can give a good way to compare associations across a number of procedures. For that reason it's a good idea to always include correlations in your analyses.
However, there are also some more specialized procedures that are helpful to use and we will turn to those next.
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