Pearson Correlation Analysis
Measuring the strength and direction of linear relationships between quantitative variables — an essential prerequisite step performed before running multiple linear regression in SPSS to identify potential multicollinearity risk early.
The Pearson correlation coefficient (denoted as $r$) is a statistical measure used to quantify the strength and direction of a linear relationship between two quantitative variables. A linear relationship is one where, when plotting the observed values of two variables on an $Oxy$ coordinate plane, the data points tend to gather along a straight line.
Visualizing Scatter Plot Trends According to the Value of $r$
($r = 1$)
($0.5 \le r < 1$)
($r \approx 0$)
($-1 < r \le -0.5$)
($r = -1$)
Pearson correlation analysis serves two critical filtering and diagnostic purposes in quantitative models:
| Analysis Objective | Value Added to the Research Model |
|---|---|
| Verifying Linearity | Confirms early whether there is a statistically significant linear correlation between independent variables and the dependent variable before entering them into the regression model. If no correlation exists (Sig. > 0.05), that relationship is excluded from the start. |
| Early Multicollinearity Check | If any two independent variables share an excessively strong linear correlation ($r \ge 0.7$ or $0.8$), it stands as a critical warning sign of data redundancy and severe multicollinearity (Multicollinearity). |
To confidently conclude that two variables possess a linear correlation and to accurately assess its strength, researchers must proceed sequentially through the following two filtering layers:
Criterion 1 — Statistical Significance (Sig. 2-tailed value)
Before interpreting the correlation coefficient $r$, we must verify if the relationship is statistically significant. Assuming a standard significance level of $5\%$ (95% confidence level):
Criterion 2 — Correlation Strength (Absolute Value |r|)
Once the correlation is confirmed statistically significant ($Sig. < 0.05$), we evaluate its strength using the absolute value of $|r|$ based on the standard classification tiers established by Andy Field (2009):
| |r| ≥ 0.5 | Strong Correlation |
| 0.3 ≤ |r| < 0.5 | Moderate Correlation |
| 0.1 ≤ |r| < 0.3 | Weak Correlation |
| |r| < 0.1 | Very Weak Correlation |
Below is an actual bivariate correlation table generated by SPSS analyzing 4 distinct variables: SAT (Overall Satisfaction - Dependent variable), and 3 independent variables: GSE (General Self-Efficacy), WE (Work Environment), and GE (Growth & Evaluation Opportunity).
| Test Statistics | SAT (Dependent) | GSE (Independent) | WE (Independent) | GE (Independent) | |
|---|---|---|---|---|---|
| SAT | Pearson Correlation | 1 | .612** | .473** | .437** |
| Sig. (2-tailed) | 0.000 | 0.000 | 0.000 | ||
| N | 402 | 402 | 402 | 402 | |
| GSE | Pearson Correlation | .612** | 1 | .173** | .204** |
| Sig. (2-tailed) | 0.000 | 0.001 | 0.000 | ||
| N | 402 | 402 | 402 | 402 | |
| WE | Pearson Correlation | .473** | .173** | 1 | .196** |
| Sig. (2-tailed) | 0.000 | 0.001 | 0.000 | ||
| N | 402 | 402 | 402 | 402 | |
| GE | Pearson Correlation | .437** | .204** | .196** | 1 |
| Sig. (2-tailed) | 0.000 | 0.000 | 0.000 | ||
| N | 402 | 402 | 402 | 402 | |
Independent-Dependent Relationships (Passed Golden Standard)
All 3 independent variables exhibit statistically significant linear correlations with the dependent variable SAT
(since all $Sig. = 0.000 < 0.05$). Specifically, evaluating correlation strength:
• GSE correlates Strongly with SAT ($r = 0.612 \ge 0.5$).
• WE correlates Moderately with SAT ($r = 0.473$, falling within the $0.3 - 0.5$ range).
• GE correlates Moderately with SAT ($r = 0.437$, falling within the $0.3 - 0.5$ range).
This demonstrates that all independent variables are theoretically suitable to be entered into the subsequent linear regression analysis.
Multicollinearity Assessment Among Independent Variables (Perfect Safety)
Checking the cross-correlation metrics between the independent variables: GSE & WE ($r = 0.173$); GSE & GE ($r = 0.204$); WE & GE ($r = 0.196$). Even though these cross-relationships show statistical significance ($Sig. < 0.05$), their coefficients are exceptionally low ($r < 0.30$). Since no pair of independent variables reaches $r \ge 0.7$, the model is **completely safe from multicollinearity risk**.
What do the double asterisks (**) mean?
The double asterisks (**) in the correlation table denote that the correlation is statistically significant at the $99\%$ confidence level ($Sig. < 0.01$, 2-tailed). This standard indicator automatically tags relationships with exceptionally high statistical reliability.
Adhere strictly to this standardized 7-step workflow within the SPSS interface to run an accurate bivariate correlation test:
Open the Correlation Dialog Box
On the main SPSS toolbar, navigate to the following path: Analyze > Correlate > Bivariate...
Input the Variables
Locate and select all representative variables (both independent variables and the dependent variable) from the left pane, then click the arrow button to move them into the Variables box on the right.
Select the Correlation Coefficient
Under the Correlation Coefficients group, check the default box for Pearson.
Configure Significance and Flagging
Under the Test of Significance section, check Two-tailed. Ensure the checkbox for Flag significant correlations remains checked so SPSS automatically marks statistically significant relationships with asterisks.
Manage Missing Data (Options Panel)
Click the Options... button on the right. In the Missing Values group, select Exclude cases pairwise. This optimizes sample size by only excluding a respondent from a specific calculation pair where a value is actually missing, instead of discarding their entire dataset. Click Continue.
Run the Calculation
Click OK to run the correlation algorithm and output the results directly to the Output Viewer window.
Generate Scatter Plots (Pro-Tip)
Visually verify your linear relationship assumption by navigating to: Graphs > Chart Builder > Scatter/Dot. Drag the independent variable to the X-axis and the dependent variable to the Y-axis to inspect the distribution structure of the raw data.
The following logical flowchart outlines the professional diagnosis process and analytical decisions when dealing with real-world correlation outcomes: