SPSS Correlation Test
SPSS correlation test is a procedure for testing whether two metric variables are linearly related in some population. The extent to which they are is usually expressed by a number, called the correlation coefficient. There are a number of different correlation coefficients but “correlation” usually means product moment correlation coefficient, better known as “Pearson correlation” (unless otherwise specified). The null hypothesis implies that no linear relation whatsoever is present in between the variables, which implies a correlation of 0. The figure below illustrates the basic idea.
SPSS Correlation Test Example
A policy maker wants to know whether age and nett monthly income are related in any way. She asks 30 respondents, resulting in age_income.sav. Do these data render it likely that age and income are related in the research population? The syntax below opens the data.
cd 'd:downloaded'. /*or wherever data file is located.
*2. Open data.
get file 'age_income.sav'.
1. Quick Data Check
Before running any statistical tests, we first want to have an idea of what the data basically look like. A nice option here is a scatter plot. The screenshots walk you through running one.
We'll first navigate to
Next, we select
income to and
age to .
Clicking results in the syntax below.
GRAPH/scatter age with income.
Resulting Scatter Plot
In this case, the scatter plot looks plausible. All respondents have an
age between, say, 20 and 68. The ages are reasonably spread out with an average around 45. Next,
income ranges from roughly €1000,- through €4500,-. This is the kind of range we'd expect for monthly income in a developed country.
On top of how
age and income
income are distributed separately, we also see that older respondents tend to have higher incomes. This indicates a positive correlation between age and income.
2. Assumptions Correlation Test
Interpretation of the correlation coefficient itself doesn't require any assumptions. However, the significance test for a correlation does make some basic assumptions. These are
- independent observations (or, more precisely, independent and identically distributed variables);
- the sample size is reasonably large (say N > 30);
3. Run SPSS Correlation Test
The screenshot shows the standard way to obtain correlations. However, this produces messy syntax and output so we'll do it differently; we could just type and run
correlations age income.
We think this is a faster and cleaner way to obtain a full correlation matrix.Note that you can use the TO and ALL keywords in this command if you have multiple variables. A better alternative, resulting in cleaner output, is using the
WITH keyword as shown in the syntax below.Insofar as we know, this clean output cannot be obtained from the menu.
correlations age income.
*2. Custom correlation matrix.
correlations age with income.
4. SPSS Correlation Test Output
The correlation itself is .730. This indicates a strong (positive) linear relationship between age and income;
The p-value, denoted by “Sig. (2-tailed)”, is .000. If the correlation is 0 in the population, then there's a 0% chance of finding the correlation we found in our sample. The null hypothesis is often rejected if p < .05. We conclude that the correlation is not 0 in the population (we now expect it to be somewhere near .73).
More precisely, since this is a 2-tailed test, the p-value consists of a 0% chance that the sample correlation is larger than .73 and another 0% chance that it's smaller than -.73.
The results are based on N = 30 cases. Since this corresponds to our sample size, we conclude that there are no missing values in our data.
5. Reporting a Correlation Test
When reporting a correlation test, the correlation itself and the N on which it's based are mandatory. Regarding the significance test, a short way of reporting it is “A strong linear relation was observed between age and income, Pearson correlation = .73, p = .000 (2-sided).” Now, there are multiple ways of calculating a p value for a correlation. By reporting like we just did, it's not obvious which method was used. SPSS uses a t-test here but -unfortunately- omits the t-value and degrees of freedom.The formulas that SPSS uses here are found under We built an .SPSS custom dialog for obtaining them, which can be freely downloaded from t-test for Pearson correlation tool.
In our case, it prints the following to our output viewer:
We can now make clear how we arrived at our p value by reporting “We found a Pearson correlation of .73; t(28) = 5.7, p = .000 (2-sided)”.