# SPSS Tutorials

BASICS REGRESSION T-TEST CHI-SQUARE TEST ANOVA

# SPSS Correlation Test – Simple Tutorial

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.

*1. Set default directory.

*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 Graphs Legacy Dialogs Scatter/Dot...

Next, we select Simple Scatter and
click
We move `income` to Y Axis and
`age` to X Axis.
Clicking results in the syntax below.

*Run scatter plot of age versus income.

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

1. independent observations (or, more precisely, independent and identically distributed variables);
2. 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.

*1. Full correlation matrix.

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 underHelp Algorithms. 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)”.

# Let me know what you think!

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# This tutorial has 30 comments

• ### By Americas Nation on September 18th, 2016

This is the best explanation I've found.

• ### By MADINGOU on September 12th, 2016

Je suis intéressé et souhaite recevoir d'avantage pour le renforcement de mes capacités en analyse et traitement de données

• ### By Ruben Geert van den Berg on September 12th, 2016

Hi Janice! If your variables aren't listed in the dialog box, it's probably because they're string variables. You can check this by just running

`correlations [variable names go here].`

This line of syntax will generate an error instead of correlations if one or more variables are strings. If so, the easiest way to convert them to numeric variables is AUTORECODE.

Hope that helps!

• ### By Janice on September 11th, 2016

Hi! Is there any way how one can carry out the Pearson correlation test with variables such as gender and fracture frequency, where both variables are listed as 1/2 (M/F) and 0/1 (no/fracture present). I tried it already on SPSS but they are not listed on the dialog box. Thanks!

• ### By Ruben Geert van den Berg on August 4th, 2016

Hi Justin! Thanks so much for your compliments! For now, keep an eye on our homepage as that's where we'll present all our new tutorials.

On the short term, we're going to cover some nonparametric tests and then we'll come up with a guide as to which test to use in which situation but the latter tutorial may take us a while.

We're also planning on launching a Youtube channel and a Facebook page but that may also take some months. Until then, please bear with us.