📊 2. Scatterplots & Significance

📊 What Is a Scatterplot?

A scatterplot is a graphical representation of the relationship between two continuous variables.

• The x-axis shows one variable.

• The y-axis shows the other.

• Each dot = one case (participant, observation, etc.)

🖼️ Visual A: Scatterplot Layout

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🔍 Why Use Scatterplots?

Scatterplots help you:

• Check linearity before computing Pearson r

• Spot outliers

• Understand the strength and direction of the relationship

📌 Good Practice: Always look at a scatterplot before interpreting r or p-values!

🧭 Patterns to Look For

🖼️ Visual B: Correlation Patterns
(Insert small scatterplots showing each pattern with r values)

✅ Statistical Significance of Pearson r

After calculating Pearson's r, you also need to check if the result is statistically significant using a p-value.

• p < .05 → the correlation is statistically significant

• p ≥ .05 → the correlation is not significant (may be due to chance)

🧪 Example (SPSS output snippet):

Interpretation: The correlation between motivation and GPA is moderate and significant; stress and sleep are weakly related and not significant.

⚠️ Important Notes on Significance

• Significance depends on sample size:

  • With large N, even small r can be significant.

  • With small N, even large r might not be.

• Always report both:

  • The value of r

  • The significance (p)

📝 APA-style report:

There was a moderate positive correlation between motivation and GPA, r(78) = .44, p = .003.

📦 Summary Box