Correlation Analysis Guide: Pearson vs. Spearman (With SPSS Steps)

Correlation analysis measures the strength and direction of the relationship between two variables. It is one of the most fundamental statistical techniques in research — used in virtually every discipline from psychology to business analytics. The two most common types are Pearson and Spearman correlation.

Pearson vs. Spearman: Which to Use

Feature	Pearson (r)	Spearman (rₛ)
Variable type	Both continuous (interval/ratio)	Ordinal or continuous
Relationship type	Linear only	Monotonic (linear or curved)
Distribution	Assumes normality	No normality assumption
Outliers	Sensitive to outliers	Robust to outliers

Simple rule:

• Use Pearson when both variables are continuous and approximately normally distributed
• Use Spearman when variables are ordinal, non-normally distributed, or when you suspect outliers

Assumptions for Pearson Correlation

1. Both variables are continuous (interval or ratio scale)
2. Linear relationship — check with a scatter plot
3. Bivariate normality — both variables should be approximately normally distributed
4. No significant outliers — outliers can dramatically inflate or deflate Pearson's r
5. Homoscedasticity — the spread of data points should be roughly consistent across the range

Spearman correlation only requires monotonic relationship and ordinal-level data — making it far more flexible.

Running Pearson Correlation in SPSS

Step-by-Step

1. Go to Analyze → Correlate → Bivariate
2. Move both variables into the Variables box
3. Under Correlation Coefficients, check Pearson (checked by default)
4. Check Flag significant correlations
5. Click OK

Output

SPSS produces a correlation matrix showing:

• Pearson Correlation (r): The correlation coefficient (-1 to +1)
• Sig. (2-tailed): The p-value
• N: Number of cases

Running Spearman Correlation in SPSS

The steps are identical, except:

1. Go to Analyze → Correlate → Bivariate
2. Move variables into the Variables box
3. Uncheck Pearson and check Spearman
4. Click OK

Interpreting the Correlation Coefficient

The coefficient ranges from -1 to +1:

• +1: Perfect positive relationship (as X increases, Y increases)
• 0: No relationship
• -1: Perfect negative relationship (as X increases, Y decreases)

Effect Size Guidelines (Cohen, 1988)

r Value	Interpretation
.10 – .29	Small
.30 – .49	Medium
.50 – 1.0	Large

These are guidelines, not rigid rules. A "small" correlation in one field may be meaningful in another.

Statistical Significance

• p < .05: The correlation is statistically significant — unlikely to be zero in the population
• p ≥ .05: The correlation is not statistically significant

Important: Statistical significance does not equal practical significance. With large samples (N > 500), even tiny correlations (r = .08) can be statistically significant. Always consider the effect size alongside the p-value.

Correlation Matrix

When analyzing relationships among multiple variables, run a full correlation matrix:

1. In SPSS, add all variables of interest to the Variables box
2. SPSS outputs a table showing every pairwise correlation

This is useful for:

• Exploring relationships before regression analysis
• Checking for multicollinearity (predictors that are too highly correlated, r > .80)
• Identifying which variables are worth investigating further

Visualizing Correlations

Always create a scatter plot before interpreting a correlation:

1. Go to Graphs → Chart Builder
2. Select Scatter/Dot → Simple Scatter
3. Drag variables to the X and Y axes
4. Click OK

Look for:

• Linear pattern: Suitable for Pearson
• Curved pattern: Use Spearman or consider polynomial regression
• Outliers: May need removal or non-parametric approach
• No pattern: Correlation is likely near zero

APA Reporting

Pearson Correlation

There was a significant positive correlation between study hours and exam score, r(148) = .52, p < .001, indicating a large effect size. As study hours increased, exam scores tended to increase.

Format: r(df) = value, p = value. The df for Pearson is N - 2.

Spearman Correlation

A Spearman rank-order correlation was computed to assess the relationship between customer satisfaction ranking and repurchase frequency. There was a significant positive correlation, rₛ(98) = .41, p < .001, indicating a medium-to-large effect.

Correlation Matrix Table

For multiple correlations, present a correlation matrix table with:

• Variable names as both rows and columns
• Correlation values below the diagonal
• Significance markers (* for p < .05, ** for p < .01)
• Means and SDs in additional columns

Common Mistakes

1. Correlation does not imply causation — A strong correlation between ice cream sales and drowning rates does not mean ice cream causes drowning (both are caused by summer heat)
2. Ignoring the scatter plot — A correlation of r = 0 does not always mean no relationship. It could be a strong curved relationship that Pearson cannot detect
3. Using Pearson with ordinal data — Likert scale items (1-5) are ordinal. Use Spearman or create composite scales before using Pearson
4. Reporting only significance — Always report the correlation coefficient AND the p-value. A significant p-value alone is meaningless without knowing the strength of the relationship
5. Over-interpreting small correlations — An r = .15 means the variables share only about 2% of their variance (r² = .0225)

What Comes After Correlation?

Correlation is often a stepping stone to more advanced analysis:

• Multiple regression: If you find several significant correlations with an outcome variable, use regression to test which predictors matter most
• Partial correlation: Control for a third variable to see if the relationship holds
• Mediation analysis: Test whether a third variable explains the mechanism behind a correlation

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