Calculate spearman coefficient of correlation 
X 15 10 20 28 12 10 16 18
Y 16 14 10 12 11 15 18 12

The formula for the Spearman rank correlation coefficient is:

\[
r_s = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}
\]

Where:
- \( d_i \) is the difference between the ranks of corresponding values of \( X \) and \( Y \).
- \( n \) is the number of observations.

### Step-by-step process:

1. Rank the values of \( X \) and \( Y \) separately.
2. Calculate the difference \( d_i \) between the ranks of each pair.
3. Square the differences \( d_i^2 \).
4. Substitute the values into the formula.

Let's start by calculating the ranks for \( X \) and \( Y \).

### Ranking:

**X: 15, 10, 20, 28, 12, 10, 16, 18**

- Ranks: 3, 1.5, 6, 8, 2, 1.5, 4, 5

**Y: 16, 14, 10, 12, 11, 15, 18, 12**

- Ranks: 7, 5, 1, 3.5, 2, 6, 8, 3.5

Now let's calculate \( d_i \), \( d_i^2 \), and use the formula.The Spearman rank correlation coefficient is approximately \(-0.33\). This indicates a weak negative correlation between \(X\) and \(Y\), meaning that as the values of \(X\) increase, the values of \(Y\) tend to decrease slightly.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How does Spearman's rank correlation differ from Pearson's correlation?
2. What would the Spearman coefficient be if the ranks were perfectly correlated?
3. How do tied ranks affect the calculation of Spearman's correlation?
4. Can Spearman's rank correlation detect nonlinear relationships?
5. When should you prefer Spearman's correlation over Pearson's?

**Tip**: Spearman's rank correlation is ideal when dealing with ordinal data or when the relationship between variables is not linear.

Calculate Spearman coefficient of correlation X 15 10 20 28 12 10 16 18 Y 16 14 10 12 11 15 18 12

Learn how to calculate the Spearman rank correlation coefficient for the data sets X = [15, 10, 20, 28, 12, 10, 16, 18] and Y = [16, 14, 10, 12, 11, 15, 18, 12]. This problem covers ranking methods, calculating rank differences, and the Spearman correlation formula. Suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation