Week 4 Lecture Recording
Introduction to Correlation Analysis
Overview of the correlation analysis.
Focus on simple correlation analysis and advanced forms such as partial and semi-partial correlations.
Importance of understanding Pearson correlation coefficients.
Correlation Design
Purpose: Measure the relationship or degree of association between two variables.
Example 1: Height and weight generally increase together.
Example 2: Increased chocolate consumption may correlate with increased spots, but is less clear.
Key Terms:
Correlated: Variables tend to covary which means scores change together in a predictable fashion.
Bivariate correlation: Examines relationships between two variables.
Spurious Correlations and Misleading Relationships
Warning against assuming causation from correlation.
Example: Ice cream consumption and happiness show correlation, but does not imply causation.
Example: Hat size has no correlation with intelligence.
Example: Waist size and junk food consumption likely show correlation.
Discuss the absurd correlation found between Nicolas Cage films and drowning incidents as an example of spurious correlation.
Understanding Correlation Coefficients
Correlation analysis provides two main insights:
Direction of the relationship (positive, negative, or none).
Magnitude (strength) of the relationship, indicated by the correlation coefficient (r).
Correlation Coefficient Scale:
Ranges from -1 to +1.
0 indicates no correlation, while +1 indicates perfect positive correlation and -1 indicates perfect negative correlation.
Examples of Correlation Relationships
Positive correlation: Height and weight (increase in height correlates with increase in weight).
Negative correlation: Increased screen time may correlate with decreased motivation.
No correlation: Hair length compared to mood shows scattered results (no clear pattern).
Calculating Correlation Coefficients
Example procedure:
Measure variables (e.g., crisps consumed versus number of adverts seen).
Compute means and deviations from the mean.
Use these deviations to calculate the correlation coefficient (ex: r = 0.62).
Estimation of shared variance by squaring the correlation coefficient.
Interpretation of Correlation Outputs
Explanation of output from statistical analysis software (e.g. JASP, jamovi):
Reporting the correlation coefficient along with significance (e.g., r = 0.72, p < 0.05).
Use of Cohen's guidelines for effect size interpretation:
0.1: Small, 0.3: Moderate, 0.5+: Large correlation coefficients.
Advanced Correlation Types
Partial Correlation: Measures the relationship between two variables while controlling for a third variable that affects both.
Semi-Partial Correlation: Similar but only controls the effect of one variable on one of the original two variables.
Example of Partial vs. Semi-Partial Correlation
Partial example with storks and birth rate controlled for area size.
Semi-partial example only controlling area effect on either storks or birth rate.
Point Biserial vs. Biserial Correlation
Point Biserial Correlation: Correlates a continuous variable with a naturally binary variable.
Example: Effects of two drugs on a health outcome (binary category).
Biserial Correlation: Applies to an underlying continuous variable leading to categorical splits.
Example: Classifying depression levels as high or low based on arbitrary cut-offs.
Visualizing and Reporting Results
Examples provided to illustrate correlations visually.
Emphasis on interpreting correlation data effectively.
Future Topics
Upcoming sessions will cover multiple regression analysis.
Practical applications and software tutorials will be provided in upcoming labs.