Pearson’s correlation (Pearson product-moment correlation; Pearson’s r) is used to determine the strength and direction of a linear relationship that might exist between two continuous variables.
The value of Pearson’s correlation is between +1 and −1. 1 is a perfect positive linear correlation and −1 is a perfect negative linear correlation. 0 is no linear correlation.
By Kiatdd (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons
Assumptions underpinning Pearson’s Correlation:
- the variables are continuous
- the variables are paired (each item has two values, one for each variable)
- there is an assumed linear relationship between the variables (typically done by visually inspecting a scatter plot of the data; if the data is not linear options include to transform data, use the non-parametric test of Spearman’s)
- the data is normally distributed (test for normality)
- their are no significant outliers (Pearson’s correlation can be heavily influenced by outliers; need to keep or remove outliers with justification)
Mathematics:
The mathematical formula for Pearson’s Correlation is:
Using the formula:
Using SPSS for Pearson’s Correlation:
Interpretation of Pearson’s Correlation:
Two steps:
1) Strength and direction of association:
No strict rules, but generally considered:
Strong correlation: .5 to 1.0 or -0.5 to 1.0.
Moderate correlation: .3 to .5 or -0.3 to .5.
Weak correlation: .1 to .3 or -0.1 to -0.3.
2) Statistical significance (reject or accept null hypothesis)
Commentary:
- Correlation is not causation, so interpret Pearson’s correlation in that context
- Pearson’s correlation is considered not robust as it is very sensitive to outliers
Related Topics:
Assumptions for Statistical Testing
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