Concurrent Deviation Method

The Concurrent Deviation Method is a simple technique to measure correlation when detailed numerical calculations (like ΣX, ΣY, ΣXY) are not possible or when changes in values matter more than actual magnitudes.

It is mainly used when:

• Data is rough, approximate, or not very precise.
• Only direction of movement (increase or decrease) is available.
• We need a quick estimate of correlation.

Meaning

This method studies whether the movements (deviations) of two variables occur in the same direction or in opposite directions.

If both variables move:

• Up together → positive sign (+)
• Down together → positive sign (+)
• Opposite directions → negative sign (–)

The correlation depends on how many times the signs agree (concurrent deviations).

Formula

r = ± √[(2c − n) / n]

Where:

• c = number of concurrent deviations (same direction)
• n = number of deviations (pairs)
• Sign of r depends on the sign of the majority deviations

Value lies between –1 and +1.

Steps of Concurrent Deviation Method

1. Calculate deviations of X (change from previous value).
2. Calculate deviations of Y similarly.
3. Assign signs (+ / –) based on direction.
4. Count c = number of times both signs are same.
5. Apply the formula.
6. Interpret the value.

Solved Example

Find correlation using Concurrent Deviation Method.

Step 1 & 2: Compute Deviations & Signs

Step 3: Count Concurrent Deviations

Same signs occur in:

• Year 2 → (+, –) → No
• Year 3 → (+, +) → Yes
• Year 4 → (–, –) → Yes
• Year 5 → (+, +) → Yes

Total concurrent deviations:

c = 3

Number of deviations:

n = 4

Step 4: Apply Formula

r = ± √[(2c − n) / n]

r = ± √[(2×3 − 4) / 4]

r = ± √[(6 − 4) / 4]

r = ± √(2 / 4)

r = ± √0.5

r ≈ ±0.707

Step 5: Decide Sign

Since most deviations were positive, r is positive.

Final Answer:

r ≈ +0.707

Moderately strong positive correlation.

Advantages

• Very simple and quick
• Useful for rough or approximate data
• No complex calculations required
• Works even when actual numerical data is unavailable

Limitations

• Only considers direction, not magnitude
• Less accurate than Pearson or Spearman
• Cannot detect non-linear patterns
• Sensitive to series with frequent fluctuations

Summary

• Concurrent deviation focuses on direction of movements, not values.
• Formula: r = ± √[(2c − n) / n]
• More concurrent deviations → stronger correlation
• Suitable for rough estimates and preliminary analysis

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