Reference · Statistics

stats.correlation

stats.correlation(list, list, str=) -> float

What it does

Pearson's correlation coefficient of two lists of numbers of the same length, from -1 to 1, as Python's statistics.correlation: 1 when the pairs lie on a rising line, -1 on a falling one, 0 when there is no linear relation. The method is "linear" by default; "ranked" gives Spearman's rank correlation, which measures whether the pairs rise together at all, line or not, by correlating their ranks (ties share their average rank).

Examples

let x = [1, 2, 3, 4, 5, 6, 7, 8, 9]let y = [1, 2, 3, 1, 2, 3, 1, 2, 3]let z = [9, 8, 7, 6, 5, 4, 3, 2, 1]print(stats.correlation(x, x), stats.correlation(x, z), stats.correlation(x, y))print(stats.correlation([1, 2, 3, 4], [1, 4, 9, 16]))print(stats.correlation([1, 2, 3, 4], [1, 4, 9, 16], "ranked"))

1.0 -1.0 0.316227766016837940.98437403869769721.0

Edge cases

• The answer is clamped to -1 to 1, so rounding cannot push it past.
• An outlier pulls Pearson's down but not Spearman's: [1, 2, 3, 4, 100] against [1, 2, 3, 4, 5] is exactly 1 ranked.
• null for the method means "linear".
• Two points are enough, and they always correlate at 1 or -1.
• Ints and floats can mix.

print(stats.correlation([1, 2, 3, 4, 5], [1, 2, 3, 4, 100]))print(stats.correlation([1, 2, 3, 4, 5], [1, 2, 3, 4, 100], "ranked"))print(stats.correlation([1, 2, 2, 3], [1, 3, 2, 4], "ranked"), stats.correlation([1, 2], [5, 3.5], null))

0.72499943359441371.00.9486832980505138 -1.0

Errors

A constant list is a runtime error, not an error value, since its correlation is not defined. So are lists of different lengths, fewer than two points, a method other than "linear" or "ranked", and an item that is not a number.

print(stats.correlation([1, 2, 3], [5, 5, 5]))

line 1: `stats.correlation`: at least one of the inputs is constant

print(stats.correlation([1, 2, 3], [1, 2, 3], "spearman"))

line 1: `stats.correlation`: unknown method "spearman" (linear or ranked)

print(stats.correlation([1], [1]))

line 1: `stats.correlation` requires at least two data points

Chaining

In a pipeline the first list comes first and the second is the argument:

let ads = [10, 20, 30, 40]let sales = [110, 190, 310, 390]print(ads | stats.correlation(sales) | round(4))print(ads | stats.correlation(sales, "ranked"))

0.99651.0

See also

stats.covariance, stats.linear_regression, stats.rank

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