How To Calculate Spearman Correlation Coefficient In Excel

Calculate the Spearman’s rank correlation coefficient (ρ) between two variables directly from your Excel data. Enter your paired data points below to compute the non-parametric measure of rank correlation.

Complete Guide: How to Calculate Spearman Correlation Coefficient in Excel

The Spearman rank correlation coefficient (ρ, “rho”) is a non-parametric measure of rank correlation that assesses how well the relationship between two variables can be described using a monotonic function. Unlike Pearson’s correlation, Spearman’s ρ doesn’t assume linear relationships or normally distributed data, making it ideal for ordinal data or non-linear relationships.

Key Advantages of Spearman’s ρ:

• Works with ordinal data (ranks) and continuous data
• Not affected by outliers (unlike Pearson’s r)
• Measures any monotonic relationship (not just linear)
• Non-parametric – no distribution assumptions

When to Use Spearman Correlation in Excel

Use Spearman’s rank correlation coefficient when:

• The data doesn’t meet Pearson correlation assumptions (normality, linearity)
• You’re working with ordinal data (e.g., survey responses on Likert scales)
• The relationship appears monotonic but not necessarily linear
• Your data contains outliers that might skew Pearson’s r
• Your sample size is small (n < 30)

Step-by-Step: Calculating Spearman’s ρ in Excel

Method 1: Using Excel’s Built-in Function (Excel 2013+)

1. Organize your data: Place your two variables in adjacent columns (e.g., A and B)
2. Use the CORREL function for ranks:
   1. Create a new column for ranks of Variable X (Column C)
   2. Use =RANK.AVG(A2,$A$2:$A$100,1) to calculate ranks
   3. Repeat for Variable Y in Column D
   4. Then use =CORREL(C2:C100,D2:D100) on the ranks
3. Alternative direct formula: For Excel 2016+, you can use:

   =CORREL(RANK.AVG(A2:A100,A2:A100,1),RANK.AVG(B2:B100,B2:B100,1))

Method 2: Manual Calculation (Understanding the Formula)

The Spearman correlation formula is:

ρ = 1 – [6∑d² / n(n² – 1)]

Where:

• d = difference between ranks of corresponding X and Y values
• n = number of observations
• ∑d² = sum of squared differences between ranks

1. Assign ranks: Rank each variable separately from 1 (smallest) to n (largest)
2. Calculate differences (d): Subtract Y ranks from X ranks for each pair
3. Square differences: Create a column for d² values
4. Sum squared differences: Calculate ∑d²
5. Apply formula: Plug values into the Spearman formula

Pro Tip:

For tied ranks (equal values), assign the average rank. For example, if two values tie for 3rd place, assign both rank 3.5.

Interpreting Spearman Correlation Results

ρ Value Range	Interpretation	Strength of Relationship
0.90 to 1.00 (-0.90 to -1.00)	Very high positive (negative) correlation	Very strong
0.70 to 0.90 (-0.70 to -0.90)	High positive (negative) correlation	Strong
0.50 to 0.70 (-0.50 to -0.70)	Moderate positive (negative) correlation	Moderate
0.30 to 0.50 (-0.30 to -0.50)	Low positive (negative) correlation	Weak
0.00 to 0.30 (-0.00 to -0.30)	Negligible correlation	Very weak/none

Testing for Statistical Significance

To determine if your Spearman correlation is statistically significant:

1. State your hypotheses:
   • H₀: ρ = 0 (no correlation)
   • H₁: ρ ≠ 0 (correlation exists)
2. Choose significance level (α) – typically 0.05
3. Find critical value from Spearman rank correlation critical values table (NIST)
4. Compare absolute value of your ρ to critical value:
   • If |ρ| > critical value → Reject H₀ (significant)
   • If |ρ| ≤ critical value → Fail to reject H₀ (not significant)

Spearman Critical Values (Two-Tailed Test) for Selected Sample Sizes

Sample Size (n)	α = 0.05	α = 0.01
5	1.000	–
6	0.886	1.000
10	0.648	0.794
15	0.521	0.654
20	0.447	0.567
30	0.364	0.465

Common Mistakes to Avoid

• Using Pearson when you should use Spearman: Always check your data distribution and relationship type first
• Ignoring tied ranks: Always use average ranks for tied values to maintain accuracy
• Small sample size issues: Spearman becomes less reliable with very small samples (n < 5)
• Misinterpreting significance: Statistical significance ≠ practical significance
• Data entry errors: Always double-check your Excel data ranges

Advanced Applications in Research

Spearman’s ρ is widely used across disciplines:

• Psychology: Measuring consistency between different test versions
• Education: Correlating teaching methods with student performance ranks
• Market Research: Analyzing preference rankings without assuming interval scales
• Biology: Studying relationships between non-normally distributed physiological measures
• Quality Control: Assessing agreement between different inspection methods

Academic Resources:

For deeper understanding, consult these authoritative sources:

• St. Lawrence University: Spearman Rank Correlation Guide
• NIH: Statistical Methods for Correlation Analysis (PMC3900052)
• Laerd Statistics: Comprehensive Spearman’s ρ Guide

Excel Alternatives for Spearman Correlation

While Excel is convenient, consider these alternatives for more advanced analysis:

• R: cor(test(data$x, data$y), method="spearman")
• Python (SciPy): spearmanr(x, y)
• SPSS: Analyze → Correlate → Bivariate → Spearman
• JASP: Free alternative with excellent visualization options

Visualizing Spearman Correlation Results

Effective visualization helps communicate your findings:

1. Scatter plot with trendline: Shows the monotonic pattern
2. Ranked data plot: Plots ranks instead of raw values
3. Heatmap: For correlation matrices with multiple variables
4. Difference plot: Shows d values (rank differences)

Frequently Asked Questions

Can Spearman correlation be negative?

Yes, Spearman’s ρ ranges from -1 to +1. A negative value indicates an inverse monotonic relationship – as one variable increases, the other tends to decrease in rank.

What’s the difference between Pearson and Spearman correlation?

Feature	Pearson (r)	Spearman (ρ)
Data Type	Interval/ratio	Ordinal or continuous
Distribution Assumption	Normal distribution	No distribution assumption
Relationship Type	Linear	Monotonic (any shape)
Outlier Sensitivity	Highly sensitive	Robust to outliers
Calculation Basis	Raw values	Ranks

How many data points do I need for reliable Spearman correlation?

While Spearman can work with as few as 5 pairs, for reliable results:

• Minimum: 10-15 pairs for preliminary analysis
• Recommended: 30+ pairs for publication-quality results
• Large samples (n > 100) provide more stable estimates

For small samples (n < 10), consider exact permutation tests instead of relying on critical values.

Can I use Spearman correlation for non-continuous data?

Yes, Spearman’s ρ is particularly useful for:

• Ordinal data (e.g., Likert scale responses: Strongly Disagree to Strongly Agree)
• Ranked data (e.g., competition placements, preference orders)
• Continuous data that violates Pearson assumptions

Avoid using it with nominal/categorical data without inherent order.