Spearman rank correlation in Excel: formula and graph

This tutorial simplifies Spearman correlation, explaining how to calculate the Spearman rank correlation coefficient in Excel. While Pearson correlation analyzes linear relationships, Spearman's handles non-linear associations, making it suitable for various data types.

- Understanding Spearman Correlation

• Calculating Spearman's rho with Excel's CORREL function
• Using the traditional Spearman formula in Excel
• Visualizing Spearman correlation with Excel graphs

Spearman Correlation: The Fundamentals

Spearman correlation, a non-parametric alternative to Pearson correlation, measures the association between variables based on their ranks. Pearson correlation assesses linear relationships (constant rate of change), while Spearman's evaluates monotonic relationships (variables change together, but not necessarily at a constant rate).

When to Use Spearman Correlation

Employ Spearman correlation when Pearson correlation's assumptions are violated:

1. Non-linear relationships or non-normally distributed data.
2. At least one ordinal variable (data ranked as "first, second, third...").
3. Presence of significant outliers. Spearman's is less sensitive to outliers due to rank-based calculations.

Examples: Does higher education correlate with environmental concern? Does symptom count relate to medication adherence?

Spearman's Rho (ρ)

The Spearman correlation coefficient (ρ, or r_s) measures both the strength and direction of the ranked data relationship. Values range from -1 to 1:

• 1: Perfect positive correlation
• -1: Perfect negative correlation
• 0: No correlation

Spearman Rank Correlation Formula

The formula varies depending on tied ranks (multiple observations sharing the same rank):

For no tied ranks:

Where:

• d_i = difference between rank pairs
• n = number of observations

For tied ranks, a more complex formula (a modified Pearson's r) is used:

Where:

• R(x) and R(y) are the ranks of x and y variables.
• R(x) and R(y) are the mean ranks.

Calculating Spearman Correlation in Excel with CORREL

While Excel lacks a dedicated Spearman function, a simplified approach using CORREL is possible:

Example: Relating physical activity (minutes in gym) to systolic blood pressure.

1. Rank the data: Use the RANK.AVG function to rank both variables (physical activity and blood pressure). For example, =RANK.AVG(B2,$B$2:$B$11,0) for physical activity. Remember to use absolute cell references ($B$2:$B$11) to ensure correct ranking.

2. Calculate Spearman's rho: Use the CORREL function on the ranked data: =CORREL(D2:D11, E2:E11) (assuming ranks are in columns D and E).

This method efficiently calculates Spearman's rho regardless of tied ranks.

Calculating Spearman Correlation with the Traditional Formula

To verify the CORREL result, use the traditional formula:

1. Calculate the difference between rank pairs (d).
2. Square each difference (d²).
3. Sum the squared differences.
4. Apply the appropriate formula (with or without tied rank adjustments) to calculate ρ.

Excel formulas can streamline this process. The simpler formula (no tied ranks) can be implemented as: =1-(6*SUM(G2:G11)/(10*(10^2-1))) (assuming the sum of squared differences is in G11, and n=10).

Visualizing Spearman Correlation with Excel Graphs

Create an XY scatter chart using the ranked data. Add a trendline and display the R-squared value. The square root of R-squared gives the Pearson correlation coefficient of the ranked data, which is equivalent to Spearman's rho. The trendline's slope indicates the correlation's direction (positive or negative).

Downloadable Practice Workbook

[Link to Spearman Rank Correlation in Excel (.xlsx file)] (Note: This link would need to be replaced with an actual link to a file.)

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