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A correlation is a statistical measure that expresses the extent to which two variables are linearly related. It’s a common tool for describing simple relationships without making a statement about cause and effect. The sample correlation coefficient, r, quantifies the strength of the relationship. Correlations are also tested for statistical significance. We describe correlations with a unit-free measure called the correlation coefficient which ranges from -1 to +1 and is denoted by r. Statistical significance is indicated with a p-value. So correlations are typically written with two key numbers: r = and p = (Gravetter et al, 2021).

  • The closer r is to zero, the weaker the linear relationship.
  • Positive r values indicate a positive correlation, where the values of both variables tend to increase together.
  • Negative r values indicate a negative correlation, where the values of one variable tend to increase when the values of the other variable decrease.
  • The p-value gives us evidence that we can meaningfully conclude that the population correlation coefficient is likely different from zero, based on what we observe from the sample.
  • “Unit-free measure” means that correlations exist on their own scale: in our example, the number given for r is not on the same scale as either elevation or temperature. This is different from other summary statistics (Correlation, n.d).