Correlational Research - Quick Reference

Correlational Research

• Purpose: examine whether and how two variables change together; identify a co-relationship and potential for prediction.
• Data collection: measure/observe both variables for each participant (e.g., shyness score and happiness score from two questionnaires).
• Outcome: when one variable changes, what happens to the other?
• Example takeaway: if shy people tend to report happiness levels that relate to shyness, the two variables are related in a systematic way.

The Correlation Coefficient (r)

• Definition: a statistic that describes the strength and direction of the relationship between two variables.
• Range: $-1.00 \le r \le 1.00$
• Strength: determined by the magnitude of $|r|$; larger values indicate stronger relationships.
• Direction: determined by the sign of $r$;
  • Positive: as one variable increases, the other increases (same direction).
  • Negative: as one variable increases, the other decreases (opposite direction).
• Zero correlation: no systematic relationship between the variables.

Interpretation of r

• Positive correlation: variables move in the same direction.
• Negative correlation: variables move in opposite directions.
• Strong correlation: $|r|$ close to 1.00.
• Weak correlation: $|r|$ close to 0.00.

Scatter Plots

• Graphs that plot scores on the two variables.
• Each dot represents one person (one pair of scores).
• Visual cues help identify positive vs negative correlations and strength.

Quick Example

• Two-questionnaire study: measure shyness and happiness for each participant.
• Compute r to assess the relationship; interpret using the signs and magnitude of $r$.