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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

Common Response

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2.7 Cause and Effect

Correlation and Further Interpretation of the Correlation Coefficient

Note: if you cannot remember how to calculate and interpret the pearson’s correlation coefficient, revise 2.6 Pearson’s Correlation Coefficient.

  • Two variables which share a statistically meaningful association are said to be correlated. In Further Maths, “statistically meaningful” means they have a pearsons correlation coefficient which indicates an association (r \geq 0.25 or r \leq-0.25).
  • The strength of a correlation is the same as the strength (weak, moderate or strong) indicated by the pearsons correlation coefficient.
  • Correlation does not mean causation. Keep in mind that correlation is purely statistical and more information is needed to know the nature of the relationship between two variables (this concept is explored further in 2.8 Non-Causal Relationships).
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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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