Correlation

• Correlation analysis


  The study of the relationship between two variables
• Test-retest reliability


  Existence of relationship (Direction)
• Correlation


  Linear relationships between two variables can be represented by a straight line
• Deriving the equation of the straight line


  1. Y = bX + a

  2. Where a = Y intercept (value of Y when X = 0)

  3. b = slope of the line
• Bivariate correlations


  Relationship between two variables
• Co-related


  Variables that co-vary
• Positive relationship


  Direct relationship between variables
• Negative relationship


  Inverse relationship between variables
• High scores on one variable


  Tend to be associated with high scores on the other variable (positive relationship)
• Low scores on one variable


  Tend to be associated with low scores on the other variable (positive relationship)
• High scores on one variable


  Associated with low scores on the other variable (negative relationship)
• Perfect relationship


  All points fall on the straight line
• Imperfect relationship


  Relationship exists but not all points fall on the line
• Correlational relationship cannot automatically be regarded as implying causation
• Statistical analysis can show whether two variables are correlated, but cannot tell the reasons why they are correlated</b>
• Possible explanations for correlation between X and Y

  • The correlation between X and Y is spurious
  • X is the cause of Y
  • Y is the cause of X
  • A third variable is the cause of the correlation between X and Y
• Exploration of relationships between variables

  1. Inspection of scatter plot

  2. Pearson's r statistical test

  3. Confidence limits around r

  4. Coefficient of determination
• Zero relationship


  No linear (straight-line) relationship between two variables
• Correlation coefficient (r)


  Measures the strength between variables, ranging from 0 to -1 and 0 to +1
• Pearson's r


  Parametric test to measure linear correlation coefficient
• Assumptions of Pearson's r

  • Each variable should be continuous level
  • Data should be normally distributed
  • No outliers on either variable
  • There should be linearity and homoscedasticity
• Spearman's rho


  Used when one or both variables are only of ordinal scaling
• Extreme scores can drastically alter the magnitude of the correlation coefficient
• Correlation does not imply causation