Correlation

  • need two sets of data in order to find correlation
  • use a scatter plot to plot correlation
  • correlation looks for a relationship between two variables
    • direction
    • shape / form
    • strength / consistency
  • direction: positive or negative
    • positive: as x increases, y increases
    • negative: as x increases, y decreases
  • form / shape
    • linear: the points tend to form a straight line
  • strength / consistency: how close a correlation resembles a line can also be measured?
    • correlation of 0: no correlation
    • a perfect correlation is 1.0 or -1.0
    • a strong correlation is near 1.0 0r -1.0
  • we use correlations for:
    • prediction
    • reliability: relationship between dif applications of same test
    • validity: does it measure what it's supposed to
    • theory verification: does correlation exist
  • correlation does not prove causation
    • to prove causation, you must manipulate a variable
  • pearson correlation measures degree and direction of linear relationship between variables
    • (r)
    • r = (degree that x+y vary together) / (degree that x+y vary apart) = (covariabliity of x+y) / (variability of x+y apart)
  • sum of products
  • sum of squares
  • outliers can have significant effects on correlation (can make i stronger)
    • always check data: pearson correlation won't detect non-linear correlation
  • coefficient of determination: r^2 is the proportion of variability in one variable that is explained by the other
    • 0.01: small correlation
    • 0.09: medium correlation
    • 0.25+: large correlation
    • explains how much of one variable we can predict from the other
  • a correlation between IQ and GPA is 0.60. r^2 is 0.36. IQ can predict 36% of a college GPA