33 Measures of Association
Measures of association describe the relationship between two variables — does rainfall move with yield? Does pest pressure move against it?
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Correlation: measures the strength and direction of the association between two variables.
- Pearson’s correlation: measures the strength of a linear relationship.
- Spearman’s rank correlation: measures the strength of a monotonic relationship (not necessarily linear).
- Covariance: measures the degree to which two variables vary together, in the original units of both variables — which makes it harder to interpret directly than correlation, since its size depends on the scale of the data.
Difference Between Covariance and Correlation
Correlation is essentially a standardized version of covariance — it rescales covariance to always fall between -1 and 1, which is what makes it comparable across datasets measured in different units. Read more on this distinction →
33.1 Example in R
Rainfall (mm) and yield (tons/ha) across 15 farms in a district:
33.1.1 Scatter Plot
A correlation above 0.9 and a scatter plot with points hugging the regression line both point to a strong, close-to-linear relationship between rainfall and yield in this dataset.
33.2 Positive Correlation
A positive correlation means two variables tend to rise and fall together. Fertilizer application and yield are a natural agricultural example, up to the point of diminishing returns.
33.3 Negative Correlation
A negative correlation means one variable tends to rise as the other falls. Pest incidence and yield are a natural example: the more a field is affected by pests, the lower its yield tends to be.
A correlation close to -1 here confirms what the downward-sloping scatter plot already shows: as pest incidence rises, yield falls, consistently and closely to linearly, across these twelve farms.
Summary
| Concept | Description |
|---|---|
| Measures of Association | |
| Correlation | Measures the strength and direction of association between two variables, scaled to fall between -1 and 1 |
| Covariance | Measures how two variables vary together, in the original units of the data |
| Positive Correlation | Both variables tend to rise and fall together, e.g., fertilizer use and yield |
| Negative Correlation | One variable tends to rise as the other falls, e.g., pest incidence and yield |