After understanding the Types of Correlation, the next essential aspect in the study of correlation is to measure its Degree. The degree of correlation tells us how strong or weak the relationship is between two variables. This measurement helps to interpret whether the observed association is meaningful, negligible, or somewhere in between.
What is Degree of Correlation?
The Degree of Correlation refers to the strength or intensity of the linear relationship between two variables. It is expressed numerically using a statistical measure called the Correlation Coefficient.
Symbol and Range:
- The most common measure is Pearson’s Correlation Coefficient, denoted by r.
- It ranges between -1 to +1.
- +1 indicates a perfect positive correlation.
- -1 indicates a perfect negative correlation.
- 0 indicates no correlation (zero linear relationship).
Formula for Pearson’s Correlation Coefficient (r)
Formula:
r = (Σ(x – x̄)(y – ȳ)) / √[Σ(x – x̄)² * Σ(y – ȳ)²]
Where:
- x, y = individual values of variables X and Y
- x̄, ȳ = mean of X and Y respectively
- Σ = summation symbol
Interpretation of Correlation Coefficient (r)
The value of r gives both the direction and degree of association. Let’s classify it in logical and progressive order:
a. Perfect Correlation (r = +1 or –1)
A value of +1 indicates that two variables move together in perfect proportion and direction. A value of –1 indicates they move in exact opposite direction.
Example: If for every 1-unit increase in X, Y also increases (or decreases) by 2 units consistently, the correlation is perfect.
b. High Correlation (r = ±0.75 to ±0.99)
Indicates a strong linear relationship. The variables have a clear trend but may not move exactly in lock-step.
Example: Income and expenditure in urban families.
c. Moderate Correlation (r = ±0.50 to ±0.74)
There is a visible association, but it is not strong enough to make confident predictions.
Example: Education level and job performance.
d. Weak or Low Correlation (r = ±0.01 to ±0.49)
The relationship exists, but it is very weak. Many other factors may be influencing the variables.
Example: Daily coffee consumption and monthly salary.
e. Zero Correlation (r = 0)
No linear relationship between the variables.
Example: Shoe size and intelligence.
Degree of Correlation and Their Interpretations
| Value of r | Degree | Interpretation | Example |
|---|---|---|---|
| +1 | Perfect Positive | Exact increase in one causes exact increase in another | Marks in Maths and Physics (theoretically) |
| +0.75 to +0.99 | High Positive | Strong upward trend | Income and Spending |
| +0.50 to +0.74 | Moderate Positive | Moderate increasing trend | Experience and Job Efficiency |
| +0.01 to +0.49 | Weak Positive | Low upward association | Reading habits and monthly savings |
| 0 | No Correlation | No linear relation | Mobile brand and academic grade |
| -0.01 to -0.49 | Weak Negative | Low downward association | Age and amount of soft drink consumed |
| -0.50 to -0.74 | Moderate Negative | Moderate decreasing trend | Online time and offline reading |
| -0.75 to -0.99 | High Negative | Strong inverse relationship | Workload and leisure time |
| -1 | Perfect Negative | Exact increase in one causes exact decrease in another | Download speed and file download time (ideal case) |
Example:
Consider a sample dataset of five students showing study hours and their marks obtained:
| Student | Study Hours (X) | Marks Obtained (Y) |
|---|---|---|
| A | 2 | 40 |
| B | 3 | 55 |
| C | 4 | 65 |
| D | 5 | 80 |
| E | 6 | 90 |
This data, when plotted or calculated using Pearson’s r, will show a strong positive correlation, most likely in the range of +0.95 to +0.99.
Merits of Correlation Coefficient
- Quantifies the degree of association in a single value.
- Useful for prediction and forecasting when association is strong.
- Helps in economic, business, and social research to establish empirical relations.
Demerits / Limitations
- Only measures linear relationship; cannot detect non-linear patterns.
- Does not imply causation other variables may be involved.
- Highly sensitive to outliers; extreme values can distort results.
Important Notes for Exam
- The correlation coefficient is a dimensionless quantity (no units).
- Always interpret both the sign and magnitude of r.
- Check scatter plot before relying on r context is important.
- Always mention sample size when reporting correlation results in practical research.
Summary
The degree of correlation plays a central role in business statistics by indicating how closely two variables are related. It ranges from -1 to +1, with values near these extremes showing strong relationships, and values near 0 indicating weak or no relationship. Accurate interpretation requires not just numerical calculation, but also an understanding of the data context and graphical patterns. In business and social sciences, it serves as a foundation for advanced techniques like regression analysis and forecasting models.
In the next article, we will explore the Methods of Measuring Correlation, including Karl Pearson’s Method, Spearman’s Rank Correlation, and more.
Read: Methods of Measuring Correlation