Correlation Analysis Lecture Notes

Overview

• Definition of correlation analysis: statistical method to measure the relationship between two variables.
• Example: relationship between salary and age.
• Key objectives: 1) strength of correlation, 2) direction of correlation.
• Correlation coefficient (R): ranges from -1 to 1.

Types of Correlation

Positive Correlation

• High values of one variable accompany high values of another.
• Example: body size and shoe size.
• Positive correlation coefficient.

Negative Correlation

• High values of one variable accompany low values of another.
• Example: product price and sales volume.
• Negative correlation coefficient.

Correlation Coefficients

1. Pearson Correlation Coefficient (R)

   • Quantifies linear relationship between two metric variables.
   • Calculated using a specific equation.
   • Strength and direction conveyed through value of R.
   • Assumptions:
     • Two metric variables must be present.
     • For hypothesis testing, both variables should be normally distributed.

2. Spearman Correlation

   • Non-parametric counterpart of Pearson correlation.
   • Uses ranks instead of raw data.
   • Example: measuring reaction time and age, assigning ranks before calculation.
   • Spearman correlation coefficient (R_s) also ranges from -1 to 1.

3. Kendall's Tau

   • Measures relationship between two variables, non-parametric test.
   • Preferred when there are many ranked ties.
   • Calculated based on the number of concordant and discordant pairs.
   • Ranges from -1 to 1.

4. Point Biserial Correlation

   • Special case of Pearson correlation for dichotomous and metric variables.
   • Examples include gender and salary, or test result (pass/fail) and hours studied.
   • Ranges from -1 to 1.
   • Null hypothesis: correlation coefficient R = 0.

Correlation vs. Causation

• Causation: relationship between cause and effect.
  • Example: coffee consumption increases alertness due to caffeine.
• Correlation: indicates relationship but does not imply causation.
  • Example: correlation between ice cream sales and sunburns could be due to a third factor (sunny weather).
• Misinterpretations: correlation does not confirm a causal relationship.
• Conditions for causality:
  1. Significant correlation between variables.
  2. Chronological sequence: one event must precede the other.
  3. Controlled experiments or theoretical grounding must support claims of causality.

Conclusion

• It is crucial to distinguish between correlation and causation in statistical analysis.
• Understanding the types of correlation and their calculations aids in accurate data interpretation.