Co-efficient of Correlation and Spearman's Rank Difference Method

According to - 

Examples of correlation - 

Types of correlation 

1. Positive correlation 

2. Negative correlation 

3. Zero correlation 

4. Linear correlation 

5. Curvilinear correlation 

Coefficient of correlation (ρ) (r) 

Interpretation of correlation according to Guilford 

Spearman's Rank Difference Method 

ρ = 1 - (6 × ∑d²) / [N (N² - 1)]
where, ρ = Coefficient of correlation
d = Difference between ranks of two variables
N = Total number of measures 

Let's understand it with the help of an example -

ρ = 1 - (6 × ∑d²) / [N (N² - 1)]
ρ = 1 - (6 × 92) / [11 × (11² - 1)]
ρ = 1 - (6 × 92) / (11 × 120)
ρ = 1 - 23 / 55
ρ = 1 - 0.42
ρ = 0.58

As the value of ρ = 0.58, we can say that the series have positive moderate correlation


Let's consider another example -

ρ = 1 - (6 × ∑d²) / [N (N² - 1)]
ρ = 1 - (6 × 74.5) / [12 × (12² - 1]
ρ = 1 - (6 × 74.5) / (12 × 143)
ρ = 1 - 149 / 572
ρ = 1 - 0.262
ρ = 0.738

As the value of ρ = 0.738, we can say that the series have positive high correlation

In these types of cases we found the average of the ranks of the individuals.