The Pearson correlation coefficient (r) is a core statistical tool used to assess the strength and direction of the linear relationship between two continuous variables.

📘 Definition Box

Pearson’s r measures how closely two variables move together.

Range: –1 to +1

  • +1 = perfect positive relationship

  • 0 = no linear relationship

  • –1 = perfect negative relationship

📊 Visual 1: Example of Pearson Correlation Ranges

Correlation (r) Relationship Type Scatterplot Pattern
+0.90 Strong Positive ↗ tightly clustered upward line
+0.30 Weak Positive ↗ spread but generally upward
0.00 No Correlation •• random scatter
–0.50 Moderate Negative ↘ downward with some spread
–0.90 Strong Negative ↘ tightly clustered downward line

🖼️ [Insert 5 mini scatterplot images corresponding to each row above]

📐 Formula for Pearson Correlation (for reference)

r=∑(X−Xˉ)(Y−Yˉ)∑(X−Xˉ)2∑(Y−Yˉ)2r = \frac{\sum{(X - \bar{X})(Y - \bar{Y})}}{\sqrt{\sum{(X - \bar{X})^2} \sum{(Y - \bar{Y})^2}}}

Where:

  • X,YX, Y

    X,Y: observed values of variables

  • Xˉ,Yˉ\bar{X}, \bar{Y}

    Xˉ,Yˉ: means of variables

🧪 When to Use Pearson Correlation

Use Pearson's only when:

  • Both variables are interval or ratio scale

  • Data is normally distributed

  • Relationship is linear

⚠️ For ordinal data, use Spearman’s rho instead.

🔍 Role in Validity Testing

Pearson correlation is particularly important in construct validity analysis:

Type of Validity Role of Correlation
Convergent validity Items or scales measuring the same construct should have high r
Discriminant validity Items or constructs should not be too highly correlated (low-to-moderate r)

📌 Example: If Satisfaction and Service Quality both correlate at r = 0.85, this could indicate poor discriminant validity — they may be measuring the same thing.

🖥️ SPSS Tip Box

🧩 In SPSS, go to:
Analyze → Correlate → Bivariate → Pearson
→ Check “Pearson” and “2-tailed” options
→ Output gives r values, sig. (p) values for hypothesis testing

🧪 Rule of thumb:
If p < .05 → the correlation is statistically significant.

🧠 Remember: Correlation ≠ Causation

Even if r = 0.90, it does not mean one variable causes the other.
They may be both influenced by a third factor.

📌 Quick Summary Box

Concept Description
Pearson r Strength/direction of linear relationship
Range –1 to +1
High r (same construct) Good convergent validity
Low r (diff constructs) Good discriminant validity
Significance p < .05 means r is statistically significant
Misuse warning Don’t confuse correlation with causation
Sửa lần cuối: Chủ Nhật, 24 tháng 8 2025, 9:04 AM