STATISTICS MODULE

Pearson Correlation Coefficient (r)

Assessing the strength and direction of linear relationships between continuous variables.

Definition Box

Pearson’s r measures how closely two variables move together. It quantifies the linear relationship.

Range: -1.0 to +1.0
+1
Perfect positive relationship
0
No linear relationship
-1
Perfect negative relationship

Interactive Visualizer

Click the buttons below to see what different correlation coefficients look like on a scatterplot.

Select a value

Scatterplot pattern description

The Formula

Pearson Correlation Calculation

$$ r = \frac{\sum{(X - \bar{X})(Y - \bar{Y})}}{\sqrt{\sum{(X - \bar{X})^2} \sum{(Y - \bar{Y})^2}}} $$
X, Y Observed values
$$ \bar{X}, \bar{Y} $$ Means of variables

When to Use

  • Interval or Ratio Scale

    Both variables must be continuous.

  • Normal Distribution

    Data should follow a bell curve.

  • Linear Relationship

    The trend must be a straight line, not a curve.

For ordinal data (ranks), use Spearman’s rho.

Construct Validity

Convergent Validity

Measures of the same construct should have High r.

Discriminant Validity

Measures of different constructs should have Low/Moderate r.

Example: If Satisfaction & Service Quality have r=0.85, they might be measuring the same thing (poor discriminant validity).

SPSS Tip

Analyze → Correlate → Bivariate → Pearson

Look for Sig. (2-tailed).

Rule of thumb: If p < .05, correlation is significant.

Correlation ≠ Causation

Even if r = 0.90, it does not prove one variable causes the other. A third variable could be the cause.

Quick Summary
Concept Description
Pearson r Strength/direction of linear relationship
Range -1 to +1
Validity High r = Convergent, Low r = Discriminant
Significance p < .05 means statistically significant

Knowledge Check

If the correlation between Job Satisfaction and Salary is r = 0.15, how would you describe the relationship?