Correlation Notes

Correlation
Chapter 10

 Covariance and Correlation
What does it mean to say that two variables are associated with one another?
How can we mathematically formalize the concept of association?

 Differences between Data Handling in Correlation & Experiment
1. Summarize entire relationship
• We don’t compute a mean Y (e.g., aggressive behavior) score at each X (e.g., violent tv watching). We summarize the entire relationship formed by all pairs of X-Y scores. This is the major advantage of correlation.
2. N = number of pairs
• Because we look at all X-Y pairs at once, we have ONE sample, with N representing the number of pairs
3. Variable X and Variable Y are arbitrary
• Either variable can be X or Y. It’s arbitrary. There is no IV or DV.
4. Scatterplot
• Data are graphed as a scatterplot of pairs of scores.
--HW Q--
 The statistic that we calculate to determine the relationship between our variables is the Correlation Coefficient
 This number tells us two things about the relationship:
 Type of relationship
 Strength of relationship
 Types of Relationships
 Linear: as scores on one variable increase, scores on the other variable either increase or decrease
 Nonlinear: relationship between X and Y changes direction at some point
 U: Age & difficulty moving
 Inverted U: Alcohol consumed & feeling well
 Correlational research focuses almost entirely on linear relationships
 Strength of Relationship
 Strength: How far from zero (absolute value)
 Direction: Positive or negative
 More on Strength
 Greater variability in Y scores at each X score means a lower correlation coefficient, and, hence, a weaker relationship.
--HW Qs--
 3 Correlation Coefficients
 Pearson
 Spearman rank-order
 Point-biserial
 All between 0 and ±1.0
 Calculated differently
 Depends on scale of measurement
 Pearson Correlation Coefficient
 Describes linear relationship
 Between two interval or ratio variables
 r =
