Measures of the relationship between 2 variables: Correlation Chapter 16

Correlation Coefficient n Descriptive statistic l degree of relationship between 2 variables l 2 dependent variables l if we know value of 1 variable… how well can we predict value of other n Values of correlation coefficient l between -1 and +1 l 0 = no relationship ~

Correlation Coefficient

Scatter Diagrams n Also called scatter plots l 1 variable: Y axis; other X axis l makes no difference which way l plot point at intersection of values l look for trends n e.g., height vs shoe size ~

Scatter Diagrams Height Shoe size

Correlation Coefficient Values n Sample statistic: r population parameter:  (rho) l values: -1 < r < +1 n Scatter diagram characteristics l slope & width l determines value of r ~

Slope & value of r n Determines sign l positive or negative n From lower left to upper right l positive ~

Slope & value of r n From upper left to lower right l negative ~

Width & value of r n Magnitude of r l draw imaginary ellipse around most points n Narrow: r near -1 or +1 l strong relationship between variables n Wide: r near 0 l little or no relationship between variables ~

Width & value of r Weight Chin ups Weight Chin ups Strong negative relationship r near -1 Weak relationship r near 0

Measures of Correlation n Several different measures l depends on level of measurement n Pearson’s r l interval/ratio n Spearman’s r s l ordinal and interval/ratio n Others for nominal and different combinations of levels of measurement ~

Factors that affect size of r n Nonlinear relationships l Pearson’s r does not detect more complex relationships l r near 0 ~ Y X

Factors that affect size of r n Range restriction l eliminate values from 1 or both variable l r is reduced l e.g. eliminate people under 72 inches ~

Correlation and Causation n Causation requires correlation, but... n Correlation does not imply causation! l Does not mean 1 variable causes changes in the other n e.g. # of household appliances negatively correlated with family size l appliances as effective birth control? n Changes may be caused by a third unknown variable ~