Book Image

Applying Math with Python - Second Edition

By : Sam Morley
Book Image

Applying Math with Python - Second Edition

By: Sam Morley

Overview of this book

The updated edition of Applying Math with Python will help you solve complex problems in a wide variety of mathematical fields in simple and efficient ways. Old recipes have been revised for new libraries and several recipes have been added to demonstrate new tools such as JAX. You'll start by refreshing your knowledge of several core mathematical fields and learn about packages covered in Python's scientific stack, including NumPy, SciPy, and Matplotlib. As you progress, you'll gradually get to grips with more advanced topics of calculus, probability, and networks (graph theory). Once you’ve developed a solid base in these topics, you’ll have the confidence to set out on math adventures with Python as you explore Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Table of Contents (13 chapters)

Testing hypotheses for non-parametric data

Both t-tests and ANOVA have a major drawback: the population that is being sampled must follow a normal distribution. In many applications, this is not too restrictive because many real-world population values follow a normal distribution, or some rules, such as the central limit theorem, allow us to analyze some related data. However, it is simply not true that all possible population values follow a normal distribution in any reasonable way. For these (thankfully, rare) cases, we need some alternative test statistics to use as replacements for t-tests and ANOVA.

In this recipe, we will use a Wilcoxon rank-sum test and the Kruskal-Wallis test to test for differences between two (or more, in the latter case) populations.

Getting ready

For this recipe, we will need the pandas package imported as pd, the SciPy stats module, and a default random number generator instance created using the following commands:

from numpy.random import...