Correlation Analysis
In many analyses, the goal is not only to describe data, but to understand how variables move together. Correlation analysis examines the strength and direction of the relationship between two numerical variables.
Correlation does not imply causation. It simply measures how closely variables are related to each other.
What Is Correlation?
Correlation quantifies the degree to which two variables change together.
Correlation values range between:
- -1 → Perfect negative relationship
- 0 → No relationship
- +1 → Perfect positive relationship
The closer the value is to ±1, the stronger the relationship.
Types of Correlation
SPSS provides different correlation measures depending on data characteristics.
Pearson Correlation is used when:
- Both variables are numeric (scale)
- Data is approximately normally distributed
- The relationship is linear
Spearman Correlation is used when:
- Data is ordinal or non-normal
- The relationship is monotonic
- Outliers affect Pearson correlation
Example Dataset
Consider the following data representing study time and exam score:
| Student_ID | Study_Hours | Score |
|---|---|---|
| 1201 | 2 | 55 |
| 1202 | 4 | 65 |
| 1203 | 6 | 78 |
| 1204 | 8 | 88 |
As study hours increase, exam scores also increase, suggesting a positive relationship.
Running Correlation in SPSS (Menu)
To perform correlation analysis using the menu:
- Go to Analyze → Correlate → Bivariate
- Select the variables
- Choose Pearson or Spearman
- Click OK
SPSS produces a correlation matrix with correlation coefficients and significance values.
Running Correlation Using SPSS Syntax
CORRELATIONS
/VARIABLES=Study_Hours Score
/PRINT=TWOTAIL
/STATISTICS DESCRIPTIVES.
This syntax computes Pearson correlation and displays descriptive statistics.
Interpreting Correlation Output
Key values to interpret:
- Correlation coefficient (r) – strength & direction
- Sig. (p-value) – statistical significance
Interpretation example:
- r = 0.85 → Strong positive relationship
- p < 0.05 → Relationship is statistically significant
A strong correlation does not prove that one variable causes the other.
Common Mistakes
Beginners often misuse correlation analysis.
- Assuming causation from correlation
- Ignoring outliers
- Using Pearson on non-normal data
Always visualize data using scatterplots before interpreting correlation values.
Quiz 1
What does correlation measure?
The strength and direction of a relationship.
Quiz 2
Which correlation is used for non-normal data?
Spearman correlation.
Quiz 3
What does r = -0.70 indicate?
A strong negative relationship.
Quiz 4
Why should scatterplots be examined before correlation?
To visually assess the relationship and detect outliers.
Quiz 5
What does p < 0.05 indicate in correlation analysis?
The correlation is statistically significant.
Mini Practice
Create a dataset with:
- Hours_Worked
- Monthly_Sales
Perform:
- A scatterplot
- Pearson correlation
Interpret the strength and direction of the relationship.
Use Analyze → Correlate → Bivariate, then interpret r and p-values together.
What’s Next
In the next lesson, you will learn about Independent Samples t-test, used to compare means between two groups.