Issue: ddof Argument in pl.corr is Redundant

[fleibfried]

Description
The Polars correlation function pl.corr appears to accept a ddof argument to specify the degrees of freedom when calculating the correlation coefficient. However, the correlation coefficient should be invariant under different ddof values since it's a ratio of covariance and standard deviation times standard deviation, both of which include the same scaling factor. Therefore, the ddof argument should not be required (see also numpy.corrcoef where bias and ddof are deprecated).

Example to Reproduce

import polars as pl

# Create a sample DataFrame
df = pl.DataFrame({
    "x": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
    "y": [2.1, 2.5, 2.9, 3.6, 3.8, 4.5, 5.1, 5.3, 5.8, 6.3]
})

# Compute correlation with different ddof values
corr_ddof_0 = df.select(pl.corr("x", "y", ddof=0)).item()
corr_ddof_1 = df.select(pl.corr("x", "y", ddof=1)).item()

# Output the correlation values
print(f"Correlation between 'x' and 'y' with ddof=0: {corr_ddof_0}")
print(f"Correlation between 'x' and 'y' with ddof=1: {corr_ddof_1}")

Expected Behavior
Both correlation coefficients should yield the same value because the ddof argument should not affect the correlation result.

Expected Output:

Correlation between 'x' and 'y' with ddof=0: 0.9971627582526871
Correlation between 'x' and 'y' with ddof=1: 0.997162758252687

Suggested Changes

• Remove the ddof argument from the pl.corr function.
• If the ddof argument is retained for backward compatibility, consider adding documentation notes about its redundancy in correlation computation.

Environment

• OS: Windows 10
• Python Version: 3.10.13
• Polars Version: 0.20.22

[lukemanley]

The ddof parameter was deprecated in #20197. I think this can be closed.