Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover 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.
Preface
Basic Packages, Functions, and Concepts
Free Chapter
Mathematical Plotting with Matplotlib
Working with Randomness and Probability
Geometric Problems
Finding Optimal Solutions
Miscellaneous Topics
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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.