Analysis of associations between variables: Correlation

Correlation

• Describes the relationship between two independent variables, ranges from -1 to +1
• Discuss Causality: During the first part of the 20th Century the S&P 500 stock index showed a correlation of 0.85 with the hemlines of women’s dresses. When the overall U.S. stock market rose, the hemline of skirts on mannequins in department stores did as well. When stock prices went lower, so did the skirts. When the Dow-Jones average rose in ‘93, skirts became shorter (also see Lipstick effect)
• the Coefficient of Correlation (r) determines the strength of the relationship between two variables

Uses

• characterize the relationship between two variables with unknown dependence to determine the strength and direction of the linear association between 2 variables.

Assumptions

• variables with unknown dependence (dependent or independent variables)
• no asumptions about causality (Correlation analysis vs. Regression analysis)
• plot of X and Y
• continuous and normally distributed (recode or transform)
• confirm homogeneity of samples

How this is done

• Calculate Variance-Covariance Matrix
  • Variance = (X-) * (X-)
  • Covariance = (X-) * (Y-)
• Pearson's Product-Moment Correlation: Correlation coefficients are the standardized covariance between two variables. best used if the relationship is believed to be linear