06 Correlation

=> simplest way to look at whether two variables are associated is to look at whether they covary

• when one variable deviates from its mean we would expect the other variable to deviate from its mean in a similar way

• Positive covariance: one variable deviates from the mean and the other variable deviates in the same direction

• Negative covariance: one variable deviates from the mean and the other variable deviates in the different direction

CAREFUL: covariance is not a standardized measure => we cannot compare covariance in an objective way

r = cov / sx sy

standardized measure

Biserial and point-biserial correlations

• used when one of the variables is dichotomous (only 2 categories)

• discrete dichotomy (e.g. pregnancy) => point-biserial correlation

• continuous dichotomy (e.g. passing or failing an exam) => biserial correlation

Partical correlation

=> a correlation between 2 variables in which the effects of the other variables are held constant is known as partial correlation

=> Correlation give no indication of the direction of causality

• the third-variable problem

  • in any correlation, causality between 2 variables cannot be assumed because a third variable could affect the results

• Direction of causality

  • Correlation coefficients say nothing about which variable causes the other to change

=> measure the amount of variability in one variable that is shared by the other

R^2 = 0.19

=> Exam anxiety shares 19% of the variability in exam performance

BUT NOT: The variance in exam anxiety is accounted for by performance ! (implies causality!)