Correlation

Correlation measures the strength and direction of the linear relationship between two continuous variables.

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1. When to Use Correlation

• Exploring the relationship between height and weight

• Assessing association between study hours and test scores

• Checking the link between temperature and electricity usage

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2. Types of Correlation Coefficients

a. Pearson Correlation (r)

Measures the strength and direction of a linear relationship between two continuous variables.

• Range: -1 to +1

• Assumes normal distribution and linearity

b. Spearman Rank Correlation (ρ)

Non-parametric measure based on ranked values.

• Used when data is not normally distributed or has outliers

c. Kendall’s Tau

Another rank-based correlation measure; more robust for small samples

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3. Interpreting Correlation Coefficients

Correlation (r)	Strength
0.00–0.19	Very weak
0.20–0.39	Weak
0.40–0.59	Moderate
0.60–0.79	Strong
0.80–1.00	Very strong

• Positive value: as one variable increases, the other tends to increase

• Negative value: as one increases, the other tends to decrease

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4. Assumptions for Pearson Correlation

• Both variables are continuous

• Linearity

• Normal distribution

• No significant outliers

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5. Example (R Code)

# Pearson correlation
cor(data$height, data$weight, method = "pearson")

# Spearman correlation
cor(data$rank1, data$rank2, method = "spearman")

# Correlation test with p-value
cor.test(data$height, data$weight)

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6. Visualizing Correlation

• Scatter plots to inspect linearity

• Correlation matrices for multiple variables

# Base scatter plot
plot(data$height, data$weight)

# Correlation matrix (e.g., with corrplot package)
corrplot(cor(data[, c("var1", "var2", "var3")]))

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7. Summary

Correlation quantifies the strength of association between variables. Choose the appropriate method based on data distribution and scale. Always visualize your data to check for patterns and anomalies.