Correlation

Key concepts behind statistical correlation

• variance - how much scores deviate from the mean, on average
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• covariance - how much pairs of scores deviate from their (respective) means in the same way, on average
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How to interpret the values of the correlation coefficient r

Pearson’s correlation coefficient

• typically used with two (or more) continuous variables
  • can be used when one is categorical
• r quantifies the strength and direction of the relationship
• always has a value between -1 and 1
  • strength - absolute value of r between 0 (no relationship at all) and 1 (perfect relationship)
  • direction - the sign of r (positive or negative)
  • positive - as one variable increases, the other tends to increase
  • negative - as one variable increases, the other tends to decrease

How to read a correlation matrix

The relationship between correlation and causation

• correlation does not equal causation:
  • no distinction between cause and effect
  • no experimental manipulation (randomisation)
  • the problem of tertium quid (an unmeasured third variable that influences two other measured quantities)
• correlation - the (standardised) degree to which two variables covary
  • calculated as covariance divided by the product of the standard deviations
  • quantifies both the strength (absolute value) and direction (sign) of the relationship between -1 and 1
  • correlation is a technical term - do not say two things are correlated unless you report r as evidence