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FM Pearson's Correlation Coefficient

2.8 Non-Causal Relationships

Observed Association

  • The associations we find by collecting data and analysing are known as observed associations, as this is what we see.
  • It is worth noting an observed association does not necessarily mean there is an actual relationship between the two variables in question, or that their relationship is causal (as we will explore further in this topic).
  • An observed association may be the result of:
    • An actual relationship of some form between the variables.
    • Chance
    • Poor experimental design
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2.6 Pearson’s Correlation Coefficient

Meaning and Calculation

  • Pearson’s correlation coefficient provides a quantitative method for determining the strength and direction of a numerical association.
  • It is denoted by a lower-case r and can be calculated using the following formula:

r=\frac{\sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{(n-1) s_{x} s_{y}}

Where s_{x} and s_{y} are the standard deviations of the explanatory and response variables, respectively.

Limitations of using Pearson’s Correlation Coefficient

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