The study of Correlation helps us understand the strength and direction of the relationship between two variables. Among various methods of studying correlation, the Concurrent Deviation Method is known for its simplicity and utility in quick assessments. Though less precise than methods like Pearson’s or Spearman’s, it is especially useful when dealing with ordinal or qualitative trends and when only directional changes matter rather than exact magnitudes.
The Concurrent Deviation Method is based on the principle of examining whether the two variables move in the same direction or not. Instead of considering the exact values, this method observes the trend whether both variables are increasing or decreasing together.
Every time both variables change in the same direction (both increase or both decrease), it is called a Concurrent Deviation.
This method is a Non-Parametric Approach and is used when:
- The data is qualitative or based on ordinal trends
- Precise numerical correlation is not necessary
- A quick idea of correlation direction is needed
Steps to Calculate Concurrent Deviation
- Take two variables X and Y (both in chronological order if time series).
- Compute the change in X and Y for each time period compared to the previous period.
- Mark each change with a "+" for increase and "-" for decrease.
- Compare the signs: if both X and Y have the same sign (+/+) or (-/-), it is a concurrent deviation.
- Count the number of concurrent deviations and use the formula to calculate the coefficient of correlation.
Formula:
The formula for concurrent deviation method is:
r = ±√( (2C - n) / n )
Where:
- r = coefficient of correlation
- C = number of concurrent deviations
- n = number of pairs of deviations (usually total number of observations - 1)
The sign of 'r' is taken as positive if the majority of deviations are concurrent; negative if not.
4. Suitability and Limitations
Suitability:
- Time series data where direction of change is more important than magnitude
- Situations with qualitative assessments (e.g., whether customer satisfaction and employee morale move together)
- Very small datasets where quick insight is needed
Limitations:
- Does not measure the degree of relationship, only direction
- Ignores actual values and magnitudes
- Not suitable for scientific or high-stake financial analysis
- Accuracy decreases as sample size increases due to loss of detail
Example: Consider the following data of two variables over 7 time periods:
| Time | X | Y |
|---|---|---|
| 1 | 10 | 20 |
| 2 | 15 | 25 |
| 3 | 13 | 23 |
| 4 | 17 | 21 |
| 5 | 19 | 24 |
| 6 | 20 | 22 |
| 7 | 18 | 20 |
Now compute deviations and signs:
| Period | ΔX | Sign X | ΔY | Sign Y | Concurrent? |
|---|---|---|---|---|---|
| 2 | +5 | + | +5 | + | Yes |
| 3 | -2 | - | -2 | - | Yes |
| 4 | +4 | + | -2 | - | No |
| 5 | +2 | + | +3 | + | Yes |
| 6 | +1 | + | -2 | - | No |
| 7 | -2 | - | -2 | - | Yes |
Number of concurrent deviations (C) = 4
Number of pairs (n) = 6 (since we have 7 periods, pairs = 7 - 1 = 6)
Apply the formula:
r = ±√((2×4 - 6) / 6) = √(2 / 6) = √0.333 = 0.577
Interpretation: There is a moderate positive correlation between X and Y. The positive sign indicates that they generally move in the same direction.
Interpretation of Results
- r = +1 → Perfect positive direction (all changes are concurrent)
- r = -1 → Perfect negative direction (all changes are opposite)
- r ≈ 0 → No clear trend or correlation
- 0 < r < 1 → Some degree of positive movement
- -1 < r < 0 → Some degree of negative movement
Application Cases
- Social sciences where data is based on trends or directional changes
- Market behavior analysis where only trend movement is of concern
- Opinion-based surveys where changes are directional rather than numeric
- Initial exploratory analysis to check if more detailed correlation study is warranted
Tip
Think of a Simple Trend Line graph where both lines representing X and Y move up and down together. Every time they turn in the same direction at the same time, it adds to the concurrent count. You are not comparing how high or low they go, only whether they turn the same way.
Merits and Demerits
Merits:
- Simple and quick to calculate
- No complex mathematics involved
- Useful for ordinal and qualitative data
- Good initial diagnostic tool
Demerits
- Does not give strength or magnitude of correlation
- Limited accuracy
- Cannot detect non-directional relationships
- Not reliable for large datasets
Conclusion
The Concurrent Deviation Method offers a practical and accessible way to study correlation when dealing with directional data or qualitative assessments. While it lacks precision, its strength lies in simplicity and speed. For a student preparing for exams like UGC NET, understanding this method provides an important tool for interpreting data trends, especially in time-series or subjective research contexts.
It should be noted, however, that this method is best used as a preliminary tool and not a substitute for more robust correlation methods where data permits.