Class #13: Correlation

1. Correlations answer questions of the relationship between two variables. Scatter plots is one way of determining the form of relationship.

2. Correlation coefficient (r) quantify the linear relationship between two variables.
Pearson r: A statistical index of how 2 variables systematically relate to one another in a linear fashion.

• Range: -1 to +1
• Sign (direction): Positive/Negative
• Magnitude (0-1): the strength of the relationship
  • r =.00 not related at all
  • r =.40 weakly related
  • r = .70 moderately related
  • r =.90 strongly related
  • r = -.90 also strongly related, same magnitude as r = .90

3. Coefficient of Determination (R²): indicates the proportion of variance in one variable that is accounted for by another variable (i.e. the variance shared between variables)
R² = square Pearson’s r, to put the index on a ratio scale
e.g.: 6.25% of the variance is shared between variables with a correlation coefficient of .25

4. Good things about the correlation coefficient (r):
– Quantifies a linear relationship
– Standardizes 2 variables into 1 index
– A single stat tells the direction & strength
– Can be squared to understand in terms of variance

5. Tricky things about the correlation coefficient (r):
– Restricted Range: when the sample includes only a portion of the range of the population, the view of correlation is skewed (e.g., the relationship between the habit of playing video games and happiness will not be accurately found if you only sample people who doesn’t play video games at all. This is extreme, but you get the idea.)
– Outliers: Off-line (deflating the correlation) and On-line (inflating the correlation)

– Reliability: Less reliable a measure is, the lower the correlation (even if there’s a real high correlation in the population)
– Interpretation (see next post)