What is the difference between skew and kurtosis functions in pandas vs. scipy?

Question

I decided to compare skew and kurtosis functions in pandas and scipy.stats, and don't understand why I'm getting different results between libraries.

As far as I can tell from the documentation, both kurtosis functions compute using Fisher's definition, whereas for skew there doesn't seem to be enough of a description to tell if there any major differences with how they are computed.

import pandas as pd
import scipy.stats.stats as st

heights = np.array([1.46, 1.79, 2.01, 1.75, 1.56, 1.69, 1.88, 1.76, 1.88, 1.78])

print "skewness:", st.skew(heights)
print "kurtosis:", st.kurtosis(heights)

this returns:

skewness: -0.393524456473
kurtosis: -0.330672097724

whereas if I convert to a pandas dataframe:

heights_df = pd.DataFrame(heights)
print "skewness:", heights_df.skew()
print "kurtosis:", heights_df.kurtosis() 

this returns:

skewness: 0   -0.466663
kurtosis: 0    0.379705

Apologies if I've posted this in the wrong place; not sure if it's a stats or a programming question.

Answer 1

The difference is due to different normalizations. Scipy by default does not correct for bias, whereas pandas does.

You can tell scipy to correct for bias by passing the bias=False argument:

>>> x = pandas.Series(np.random.randn(10))
>>> stats.skew(x)
-0.17644348972413657
>>> x.skew()
-0.20923623968879457
>>> stats.skew(x, bias=False)
-0.2092362396887948
>>> stats.kurtosis(x)
0.6362620964462327
>>> x.kurtosis()
2.0891062062174464
>>> stats.kurtosis(x, bias=False)
2.089106206217446

There does not appear to be a way to tell pandas to remove the bias correction.