Pearson Correlation Coefficient Between Groups


Pearson Correlation

To illustrate how to compare correlation between two groups. The article would use dataset of Islamic.sav. The Questionnaire was designed to evaluate the factors that affect people’s attitude towards Islamic banking. There may be situation when you need to compare the correlation coefficient between two groups. For instance in this dataset, we may need to compare the responses between male and female respondents. How to do it is described below If you wish to follow along with this example, you should start SPSS and open the Islamic.sav file.

Correlation Coefficient between Two Groups

Steps to compare Correlation Coefficient between Two Groups

First we need to split the sample into two groups, to do this follow the following procedure

  1. From the menu at the top of the screen, click on Data, and then select Split File.
  2. Click on Compare Groups.
  3. Move the grouping variable (e.g. Gender) into the box labeled Groups based on. Click on OK.
  4. This will split the sample by gender.

Follow the steps in the article (Running Pearson Correlation) to request the correlation between your variables of interest. The results will be reported separately for the two groups.

It is Important to remember, when you are finished looking at males and females separately you will need to turn the Split File option off. It stays in place until you manually turn it off. To do this, make sure that you have the Data Editor Window open on the screen in front of you. Click on Data, Split File and click on the first button: Analyze all cases, do not create groups.

The output generated from the correlation procedure is shown below.

Interpretation of output from correlation for two groups

From the output given above, the correlation between ATIB and SI for males was r=.262, while for females it was slightly higher, r=.293. Although these two values seem different, is this difference big enough to be considered significant? Detailed in the next section is one way that you can test the statistical significance of the difference between these two correlation coefficients. It is important to note that this process is different from testing the statistical significance of the correlation coefficients reported in the output table above. The significance levels reported above (for males: Sig. = .000; for females: Sig. = .116) provide a test of the null hypothesis.

What might be confusing for you at this stage is that although the Correlation Coefficient for Male’s is low but it is still significant, but the coefficient for female group is slightly higher but it is still insignificant. The reason for this is the number of cases in each group. The sample size for male groups is significantly higher (N = 235) in comparison to female group (N = 30).

Statistical Significance for difference between Groups

While you now know how to find correlation coefficient in each of the groups, but still we do not know if the difference in relationship between groups is significant. This section describes the procedure that can be used to find out whether the correlations for the two groups are significantly different. Unfortunately, SPSS will not do this step for you, so it is done manually. Step by Step procedure to find out if the relationship is significantly different you can follow the following steps.

First we will be converting the r values into z scores and then we use an equation to calculate the observed value of z (zobs value). The value obtained will be assessed using a set decision rule to determine the likelihood that the difference in the correlation noted between the two groups could have been due to chance.

Before calculating the statistical significance you will check certain assumptions.

  1. It is assumed that the r values for the two groups were obtained from random samples and that the two groups of cases are independent (not the same participants tested twice).
  2. The distribution of scores for the two groups is assumed to be normal.
  3. It is also necessary to have at least 20 cases in each of the groups.

Convert each of the r values into z values

First step is to convert the correlation coefficients (r) into the Z scores. From the SPSS output, find the r value (ignore any negative sign out the front) and N for Group 1 (males) and Group 2 (females).

Males r1 =.262                    N1 =235

Females r2 =.293              N2 =30

Using the following , find the z value that corresponds with each of the r values.

Males z1 =.266

Females z2 =.304

Put these values into the equation to calculate zobs

The equation is provided below, put the respective values in the equation and make the necessary calculations.

Determine if the zobs value is statistically significant

If the zobs value that you obtained is between 1.96 and +1.96, this means that there is no statistically significant difference between the two correlation coefficients. We can only reject the null hypothesis (no difference between the two groups) only if your z value is outside these two boundaries. The decision rule therefore is:

  1. If 1.96 < zobs < 1.96: correlation coefficients are not statistically significantly different.
  2. If zobs is less than or equal to 1.96 or zobs is greater than or equal to 1.96: coefficients are statistically significantly different.

In the example above, zobs value of .206, that is between the boundaries, so we can conclude that there is a no statistically significant difference in the strength of the correlation between ATIB and SI for males and females.