Lesson 5:
Computing a Correlation and a Scatterplot
Purpose
This lesson explains how to obtain Pearson Product Moment Correlation Coefficients (r's), for pairs of variables, and tests the significance of these coefficients. This enables you to find the degree of relationship between any two continuous variables in your study. We will also describe how you can graph the relationships between your variables (i.e., create scatterplots).
An Example: Dormitory Survey
Suppose that you have collected questionnaire responses to five questions concerning dormitory conditions from 10 college freshmen. (Normally you would like to have a larger sample, but the small sample in this case is useful for illustration.) The questionnaire assesses the satisfaction with noise, furniture, study area, safety, and privacy. Assume that you have also assessed the students' family income level, and you would like to test the hypothesis that satisfaction with the college living environment is correlated with wealth (family income).
The questionnaire contains five questions about satisfaction with the various aspects of the dormitory "noise," "furniture," "space," "study," "safety," and "privacy." These are answered on a 5-point Likert-type scale (very dissatisfied to very satisfied), which are coded as 1 to 5. The data sheet for this study is shown below.
| | | | | | | |
| 01 | 19 | 5 | 5 | 4 | 5 | 5 |
| 02 | 39 | 3 | 3 | 5 | 5 | 4 |
| 03 | 55 | 2 | 1 | 2 | 2 | 2 |
| 04 | 25 | 5 | 3 | 4 | 4 | 5 |
| 05 | 75 | 1 | 2 | 2 | 1 | 2 |
| 06 | 95 | 1 | 1 | 1 | 1 | 1 |
| 07 | 47 | 3 | 2 | 4 | 3 | 3 |
| 08 | 28 | 4 | 4 | 5 | 4 | 4 |
| 09 | 120 | 2 | 2 | 1 | 1 | 1 |
| 10 | 35 | 3 | 4 | 5 | 4 | 4 |
In creating your data file, you will need to create a column for each of the different variables. In the interest of keeping track of what the variables represent, you should also type a very descriptive label for each of your variables. Try typing your SPSS data file and then compare it with the one below.
Data File for Dorm Study
Computing the Pearson Product Moment Correlation for the Dormitory Survey
Step 1. Click on Analyze, then Correlate, then Bivariate.
Step 2. Move the variables that you wish to have correlated into the Variables field.
Step 3. If you wish to print the means and standard deviations, then click on Options and select the desired statistics. Then click on Continue and then OK.
Examining the Output
Below is the major portion of the output from the dormitory survey correlations. You will see that the first table contains the descriptive statistics concerning your variables. The correlational statistics are presented in the second table. Note that SPSS computes all possible correlations among the variables that you specified. The correlations are listed in the first third of the table, the significance levels of the correlations are listed in the second third of the table, and the valid number of pairs of scores are listed in the bottom portion of the table.
Output File for the Dorm Study
Creating a Scatterplot for Pairs of Variables
A scatterplot (also called scattergrams or scatter diagrams) is a two-dimensional graphic representation of the relationship between two variables. This type of graph helps you evaluate the nature and degree of relationship between your variables.
Step 1. To create a scatterplot of your data, let us say between the variables of income and noise, click on Graphs and then Scatter.
Step 2. In the Scatterplot menu, click on Simple and then Define.
Step 3. Now move the variables into the appropriate axes. In this case, you might want to move the noise variable into the Y-Axis field and the income variable into the X-Axis field. When you have done this, click on OK, and as shown below, this should produce a scatterplot of the relationship between your two variables. As you can see, this graph tends to show declining satisfaction for those who have higher family incomes.
Initial Scatterplot Graph
Step 4. As you can see, the SPSS default options for labeling this graph are not ideal. You can modify your graph by double clicking on it, and this accesses the SPSS Chart Editor. Once you are in the SPSS Chart Editor, you can center the label on the Y axis and can capitalize the first letters of the words by double clicking on the label and then modifying the appropriate items. You can make the title fit by clicking on the title and then on Format and then on Text. With a little work, your graph can look like the one below.
Modified Scatterplot Graph
Step 5. You should realize that you can save the template for your preferred options by selecting File and then Save Chart Template. This will enable you to apply these options to future graphs.
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