Spearman Rank Correlation Coefficient Examples

Explore practical examples of Spearman rank correlation coefficient to understand its application in various fields.
By Jamie

Understanding Spearman Rank Correlation Coefficient

The Spearman rank correlation coefficient is a non-parametric measure that assesses the strength and direction of the association between two ranked variables. Unlike Pearson’s correlation, which requires a linear relationship and normally distributed data, Spearman’s method is more flexible and can be used with ordinal data or non-linear relationships. Below are three practical examples illustrating the application of the Spearman rank correlation coefficient across diverse fields.

Example 1: Academic Performance and Study Hours

In an educational context, researchers often want to understand how study habits affect academic performance. This example examines the correlation between the number of hours students study per week and their corresponding grades.

  • Context: A group of 10 high school students is surveyed regarding their weekly study hours and their final grades on a scale from 1 to 100.
Student Study Hours (Rank) Final Grade (Rank)
A 5 70
B 10 90
C 3 60
D 12 95
E 8 85
F 7 80
G 4 65
H 6 75
I 11 92
J 9 88

Calculating the Spearman rank correlation coefficient yields a value of 0.92, indicating a strong positive correlation. This suggests that students who study more hours tend to achieve higher grades.

Notes:

  • Variations can include adjusting the sample size or considering different grading methods.

Example 2: Employee Satisfaction and Productivity

In the corporate world, understanding the relationship between employee satisfaction and productivity is vital for management. This example explores how employee satisfaction scores correlate with productivity ratings.

  • Context: A company surveys 15 employees about their job satisfaction on a scale from 1 to 10 and records their productivity ratings based on quarterly performance reviews.
Employee Satisfaction Score (Rank) Productivity Rating (Rank)
1 8 90
2 3 60
3 9 95
4 5 75
5 6 80
6 7 85
7 4 70
8 10 98
9 2 50
10 1 40
11 8 88
12 6 77
13 5 72
14 4 65
15 9 94

The Spearman rank correlation coefficient for this data is calculated to be 0.85, which indicates a strong positive relationship between employee satisfaction and productivity.

Notes:

  • This analysis can be further refined by incorporating qualitative measures or expanding the sample size.

Example 3: Temperature and Ice Cream Sales

Understanding consumer behavior in relation to temperature can be crucial for businesses like ice cream shops. This example investigates how temperature affects ice cream sales.

  • Context: An ice cream shop records daily sales figures and the average temperature over a two-week period.
Day Temperature (Rank) Ice Cream Sales (Rank)
1 70°F 50
2 75°F 60
3 80°F 70
4 85°F 80
5 90°F 90
6 95°F 100
7 68°F 40
8 72°F 55
9 78°F 65
10 82°F 75
11 88°F 85
12 92°F 95
13 77°F 66
14 74°F 58
15 69°F 42

In this case, the Spearman rank correlation coefficient is calculated to be 0.93, indicating a very strong positive correlation between temperature and ice cream sales. Higher temperatures correlate with increased sales.

Notes:

  • This example can also be analyzed seasonally to assess patterns over time or across different regions.