[Python] Spearman Rank Correlation in SciPy vs. Manual Calculation - Mismatch in Results

I am trying to compute the Spearman rank correlation coefficient between two ranked lists using scipy.stats.spearmanr and manually using the formula:



However, I am getting significantly different results.

I have two lists representing the top 10 similar users identified using two different methods:

Method 1 Rankings:

User ID: [301, 597, 414, 477, 57, 369, 206, 535, 590, 418]

Rank: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

Method 2 Rankings:

User ID: [301, 477, 19, 120, 75, 57, 597, 160, 577, 369]

Rank: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

I then applied Spearman’s rank correlation using scipy.stats.spearmanr:

from scipy.stats import spearmanr

method1 = [301, 597, 414, 477, 57, 369, 206, 535, 590, 418]
method2 = [301, 477, 19, 120, 75, 57, 597, 160, 577, 369]

coef, _ = spearmanr(method1, method2)
print(f"Spearman coefficient: {coef}")

Spearman coefficient: 0.2727


Manual Calculation: To verify, I computed ρ manually using the common users between both lists.

User ID Rank (Method 1) Rank (Method 2) (d_i = R_1 - R_2) (d_i^2)
301 1 1 0 0
597 2 7 -5 25
477 4 2 2 4
57 5 6 -1 1
369 6 10 -4 16

we have only 5 common users, n=5.

Using the formula I got Spearman coefficient() = -1.3 which is out of range for Spearman’s coefficient [ − 1 , 1 ] However, scipy.stats.spearmanr() gives 0.2727, which is within range but significantly different.

Why is my manual calculation incorrect? Am I making a mistake in how I handle missing users or the ranking?

How does scipy.stats.spearmanr handle missing values or mismatched lists internally? Does it rank only common elements, or does it consider all elements?

Where is my manual approach incorrect and how scipy.stats.spearmanr internally processes the rankings?

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