Spearman Correlation

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Example: a follower count that almost doubles every month: 2, 3, 5, 9, 17, 33 and 65 thousand over seven months. The relationship with time is perfectly increasing, but it isn't a straight line. What do Spearman and Pearson say? Change the values to work out your own case.

Values of x One value per observation, separated by spaces or commas. Values of y In the same order as the x values.

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What each term means

Spearman Correlation (rₛ): From −1 to 1, it measures whether y tends to rise (or fall) as x rises, whatever the shape of the relationship. It is Pearson's correlation computed on the ranks.
One Minus the Disagreement: When the two orders match, every difference is zero and rₛ = 1. The more the orders disagree, the more is subtracted.
Rank Differences (6Σdᵢ²): dᵢ is the difference between xᵢ's position in the order of the x values and yᵢ's in the order of the y values. Using positions, not values, makes an extreme value count only as “the largest”.
Normalization (n(n² − 1)): Half the largest value 6Σdᵢ² can reach: with it, exactly reversed orders give rₛ = −1. With ties, the formula is only approximate.

When to use it, assumptions and alternatives: Spearman correlation in the statistical tests catalog.