Correlation is a statistical technique that measures the degree of relationship between two variables. Understanding correlation is essential in Business, Economics, Finance, and Social Sciences because it helps us study how changes in one variable relate to changes in another.
There are two broad methods to study correlation:
- Graphical Methods
- Algebraic (Mathematical) Methods
In this article, we will concentrate on the graphical methods of studying correlation, which form the visual foundation for understanding the nature and direction of relationships. The algebraic methods Karl Pearson’s Coefficient, Spearman’s Rank Correlation, and Concurrent Deviation Method will be discussed in the following articles.
Graphical Methods
Graphical methods provide a simple, intuitive way to get a first impression of the type and strength of correlation between two variables. The key advantage of graphical methods is that they do not require numerical calculations. However, they are not precise or quantifiable, so they are mostly used for preliminary analysis.
a. Scatter Diagram (or Scatter Plot)
The scatter diagram is the most commonly used graphical method for studying correlation. It consists of plotting paired values of two variables (X and Y) as points on a Cartesian plane.
How to Draw a Scatter Diagram:
- Take the values of the independent variable (X) on the X-axis.
- Take the values of the dependent variable (Y) on the Y-axis.
- Plot the points for each pair (X, Y).
Interpretation of Scatter Diagrams:
- Perfect Positive Correlation: All points lie on a straight line sloping upward.
- Perfect Negative Correlation: All points lie on a straight line sloping downward.
- High Degree of Correlation: Points are close to a straight line.
- No Correlation: Points are scattered with no clear pattern.
Example:
Suppose we have data on the number of hours studied and marks scored by students:
Hours (X): 2 3 4 5 6
Marks (Y): 40 50 65 70 85
When these pairs are plotted, we see an upward trend. This suggests a positive correlation between hours studied and marks obtained.
Merits of Scatter Diagram:
- Simple and easy to draw.
- Provides a visual indication of relationship.
- Does not require mathematical calculations.
Demerits of Scatter Diagram:
- Does not provide an exact numerical value of correlation.
- Only gives a rough idea of direction and strength.
Quick Visual Clues:
| Pattern | Type of Correlation |
|---|---|
| Points rise from left to right | Positive Correlation |
| Points fall from left to right | Negative Correlation |
| Points are widely scattered | No Correlation |
b. Dot Plot (Dot Chart)
A dot plot is another graphical representation of paired data. It is less commonly used than scatter diagrams but can be helpful when data sets are small. Each pair (X, Y) is plotted as a dot in a coordinate space similar to a scatter plot, but here, dots may overlap if values are repeated.
Features of Dot Plot:
- Effective when there are overlapping or identical values.
- Useful for spotting clustering and gaps in data.
Example:
Let us take another data set:
X: 1, 2, 2, 3, 3, 3
Y: 10, 20, 20, 30, 30, 30
This will result in overlapping points at (2,20) and (3,30). Dot plots are especially good at visualizing frequency of pairs.
Advantages of Dot Plots:
- Good for identifying duplicate or frequent values.
- Simple to interpret for small data sets.
Limitations:
- Not suitable for large data sets.
- Does not provide precise correlation measurement.
Brief Introduction to Algebraic Methods
While graphical methods help us visualize correlation, algebraic methods are used to calculate the exact degree of correlation using formulas. These will be explained in the following parts:
- Karl Pearson's Coefficient of Correlation - Measures linear correlation using actual values.
- Spearman’s Rank Correlation - Used for ordinal data or when values are ranked.
- Concurrent Deviation Method - A simpler, less precise method based on the direction of deviations.
Conclusion
Graphical methods of correlation provide an excellent starting point for analysis. They help us understand the nature, direction, and rough strength of the relationship between two variables without complex calculations. Among graphical tools, the scatter diagram is the most widely used and highly recommended for quick insights. Dot plots serve as an alternative when data is small or repetitive.
However, for detailed statistical analysis, we must complement graphical methods with algebraic techniques. These will be explored in the upcoming lessons.