Pandas: How to calculate unbiased skew of a Series

Introduction

Understanding the skewness of data is essential in data analysis as it helps in recognizing the distribution characteristics of a variable. Particularly, skewness measures the asymmetry of the distribution of values in a dataset. In this tutorial, we will explore how to calculate the unbiased skew of a series using the Pandas library in Python. Along the way, we will begin with the basics and gradually move to more advanced examples.

Before we dive into calculating the skewness, it’s critical to understand that the ‘bias’ in statistical terms refers to the tendency of a statistic to overestimate or underestimate a parameter. By ‘unbiased,’ we aim to adjust the skewness calculation in such a manner that it more accurately reflects the true nature of the dataset. Pandas provides a built-in function to achieve this, making it straightforward for practitioners.

Getting Started

First, ensure you have Pandas installed. You can install Pandas using pip:

$ pip install pandas

Now, let’s begin by importing Pandas and creating a simple Series object:

import pandas as pd
import numpy as np

# Creating a Series
s = pd.Series(np.random.randn(1000))

This Series, ‘s’, contains 1000 random numbers drawn from a normal distribution. The expectation here is that the distribution of these numbers is approximately symmetrical, leading to a skewness close to zero.

Calculating Skewness

To calculate the skewness, we use the .skew() method:

print(s.skew())

By default, this method applies Bessel’s correction, making the calculated skewness an unbiased estimate of the population skewness. The correction is particularly relevant for small sample sizes and aims to increase the accuracy of the skewness measure.

Exploring Skewness in Real-World Data

Let’s move to a real-world dataset to see how this works in practice. We’ll use the diamonds dataset available in the seaborn library. First, let’s load this dataset into a Pandas DataFrame:

import seaborn as sns

diamonds = sns.load_dataset('diamonds')
print(diamonds.head())

Next, we will calculate the skewness of the ‘price’ column:

print(diamonds['price'].skew())

Again, the calculation is unbiased thanks to Bessel’s correction. This step is crucial when working with data to ensure that your statistical inferences are as accurate as possible.

Advanced Application: Comparing Skewed Distributions

Let’s take it a step further. Imagine you’re working with two series of data and want to compare their skewness directly. It’s straightforward with Pandas:

# Creating two skewed Series
s1 = pd.Series(np.random.exponential(scale=2.0, size=1000))
s2 = pd.Series(np.random.beta(2, 5, size=1000))

# Calculating and comparing their skewness
print('Skewness of s1:', s1.skew())
print('Skewness of s2:', s2.skew())

The first series, ‘s1’, follows an exponential distribution, typically skewed to the right, while ‘s2’, coming from a beta distribution, might be skewed left or right depending on the parameters. This example illustrates how easy Pandas makes it to calculate and compare skewness across different data distributions.

Conclusion

In this tutorial, we explored how to calculate the unbiased skew of a Series in Pandas, starting with basic examples and moving to more complex real-world datasets. Understanding skewness and its implications is crucial for data analysis, and Pandas provides an efficient and straightforward way to calculate it accurately. By mastering these techniques, you will be better equipped to describe and analyze the distribution of your data.