To illustrate how to use Correlation I would use dataset of Islamic.sav. The Questionnaire was designed to evaluate the factors that affect people’s attitude towards Islamic banking. In this example I am interested in assessing the correlation between attitude towards Islamic banking and the Social Influence. If you wish to follow along with this example, you should start SPSS and open the Islamic.sav file.
Example on Running Pearson Correlation
The Problem:
Investigate the relationship between Social Influence and attitude to Islamic banking.
Null Hypothesis
H0:There is no association between Social Influence and Attitude towards Islamic Banking.
HA:There is an association between Social Influence and Attitude towards Islamic Banking.
Information Required:
- Two continuous variables (In this case, Social Influence and Attitude)
Assumptions for Pearson Correlation
- At least two continuous variables (Interval or Ratio) or One Continuous variable and other is dichotomous scale variable
- If there is a dichotomous variable you should, however, have roughly the same number of people or cases in each category of the dichotomous variable.
- Normal distribution for Continuous Variable
Steps to run Pearson Correlation
- Choose Analyze → Correlate → Bivariate
- Choose the variables for which the correlation is to be studied from the left-hand side box and move them to the right-hand side box labeled Variables. Once any two variables are transferred to the variables box, the OK button becomes active. We can transfer more than two variables, but for now we will stick to only two.
- Select the variable ATIB (Attitude towards Islamic Banking) and SI (Social Influence). Press the Arrow button to the add the variable to the Variables: list box
- There are some default selections at the bottom of the window; these can be changed by clicking on the appropriate boxes. For our purpose, we will use the most commonly used Pearson’s coefficient. Pearson checkbox is check from the Correlation Coefficient group box
- Next, while choosing between one-tailed and two-tailed test of significance, we have to see if we are making any directional prediction. The one-tailed test is appropriate if we are making predictions about a positive or negative relationship between the variables; however, the two-tailed test should be used if there is no prediction about the direction of relation between the variables to be tested. In this case we will stick to two-tailed test.
- Finally Flag significant correlations asks SPSS to print an asterisk next to each correlation that is significant at the 0.05 significance level and two asterisks next to each correlation that is significant at the 0.01 significance level.
- Press OK
Output
The output of the analysis is shown below, the results shows only one table
Interpretation of Output
For Pearson Correlation, SPSS provides you with a table giving the correlation coefficients between each pair of variables listed, the significance level and the number of cases. The results for Pearson correlation are shown in the section headed Correlation.
The tables shows that a total of 265 respondents. First it is important to consider is the direction of the relationship between the variables. This is identified through a negative sign in front of the correlation coefficient value? A negative sign before the correlation coefficient means that there is a negative correlation between the two variables (i.e. high scores on one are associated with low scores on the other).
The interpretation of relationship depends how the variables are scored. Checking the Questionnaire, it shows that higher scores on the construct Attitude towards Islamic Banking means positive attitude similarly higher scores on Social Influence means greater social influence. This is one of the major areas of confusion for students, so make sure you get this clear in your mind before you interpret the correlation output.
In the example given here, the Pearson correlation coefficient (.267) indicating a positive correlation between Social influence and Attitude towards Islamic Banking. The more the social influence on people with regards to Islamic banking, the positive would be the attitude of people towards Islamic banking. To determine the strength of relationship we would use the table 11.1 presented earlier, using the table the correlation matrix shows that there is a Very low Positive between the two variables.
The Correlation Coefficient can be used to assess how much variance the two variables share.
This can be done by squaring the r value (multiply it by itself) also called the Coefficient of Determination, to convert this to ‘percentage of variance’; just multiply by 100 (shift the decimal place two columns to the right).
In our example we have the coefficient value of .267, two variables that correlate to get the coefficient of determination we square the r value and the result is .0712, and the percentage of variance is 7.12. This shows that Social Influence indicates 7.12% variance in Attitude towards Islamic banking.
The next thing to consider is the significance level (listed as Sig. 2 tailed). This is a frequently misinterpreted area, so care should be exercised here. The level of statistical significance does not indicate how strongly the two variables are associated (this is given by r), but instead it indicates how much confidence we should have in the results obtained. The significance of r is strongly influenced by the size of the sample. In a small sample (e.g. n=30), you may have moderate correlations that do not reach statistical significance at the traditional p<.05 level. In large samples (N=100+), however, very small correlations (e.g. r=.267) as in our case, it may reach statistical significance. While you need to report statistical significance, you should focus on the strength of the relationship and the amount of shared variance (explained earlier).
Reporting Pearson Correlation
Pearson product correlation social influence and attitude towards Islamic banking is very low positive and statistically significant (r = 0.267).
Correlation Matrix
Correlation is often used to explore the relationship among a group of variables, rather than just two as described above. In this case, it would be awkward to report all the individual correlation coefficients in a paragraph; it would be better to present them in a table also referred to as correlation matrix. SPSS results provide the table that can be made part of the thesis.
In order to produce a correlation matrix showing relationships between more than two variables, you need to add more than two variable on which the relationships is intended to be studied. For our example we would add the 6 critical factors and attitude towards Islamic banking. Follow the steps mentioned above, add the factors between which the correlation is to be evaluated.
Press OK, the following correlation matrix is displayed in the output window.
The output gives correlations for all the pairs of variables and each correlation is produced twice in the matrix. The Correlations are repeated under the number 1 in the diagonal. You can consider the correlation in either of the diagonal. It would be better to present them in a table. One way this could be done is as follows:
In each cell of the correlation matrix, we get Pearson’s correlation coefficient that shows the strengths of the relationship, which could be evaluated using the table described earlier, the significance is shows through asterisks right next to the correlation coefficient. A Single * shows that correlation is significant at .05 (5%) while ** shows that correlation is significant at .01 (1%). From the output, we can see that the correlation coefficient between ATIB and SI is 0.267 which is very low positive and significant at .01. Similarly the correlation coefficient between ATIB and RC is 0.485 which is and is low positive and significant at .01. Results for correlations between other set of variables can also be interpreted similarly. Coefficient not having the asterisks sign are not significant related and the strength of relationship is almost negligible.
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