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# FM No Association

## 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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## 2.5 Relationships between two Numerical Variables

### Guidelines to Analysing Numerical Associations

• Begin with context: what does the data represent?
• Identify the explanatory and response variables.
• Assess the form of the association: is it linear, non-linear or is there no association.
• If it is linear, assess the strength (strong, moderate or weak). Ideally, do this using the Pearson’s correlation coefficient (detailed in 2.6 Pearson’s Correlation Coefficient), however if the raw data is not available, a qualitative assessment will suffice.
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