📘 1. Pearson Correlation Explained

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.

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📘 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

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📊 Visual 1: Example of Pearson Correlation Ranges

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

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📐 Formula for Pearson Correlation (for reference)

$r = \frac{\sum{(X - \bar{X})(Y - \bar{Y})}}{\sqrt{\sum{(X - \bar{X})^2} \sum{(Y - \bar{Y})^2}}}$

r=∑(X−Xˉ)2∑(Y−Yˉ)2

​∑(X−Xˉ)(Y−Yˉ)​

Where:

• $X, Y$

  X,Y: observed values of variables

• $\bar{X}, \bar{Y}$

  Xˉ,Yˉ: means of variables

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🧪 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.

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🔍 Role in Validity Testing

Pearson correlation is particularly important in construct validity analysis:

📌 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.

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🖥️ 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.

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🧠 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.

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📌 Quick Summary Box