#### Overview of this book

There are many algorithms for data analysis and it’s not always possible to quickly choose the best one for each case. Implementation of the algorithms takes a lot of time. With the help of Mathematica, you can quickly get a result from the use of a particular method, because this system contains almost all the known algorithms for data analysis. If you are not a programmer but you need to analyze data, this book will show you the capabilities of Mathematica when just few strings of intelligible code help to solve huge tasks from statistical issues to pattern recognition. If you're a programmer, with the help of this book, you will learn how to use the library of algorithms implemented in Mathematica in your programs, as well as how to write algorithm testing procedure. With each chapter, you'll be more immersed in the special world of Mathematica. Along with intuitive queries for data processing, we will highlight the nuances and features of this system, allowing you to build effective analysis systems. With the help of this book, you will learn how to optimize the computations by combining your libraries with the Mathematica kernel.
Mathematica Data Analysis
Credits
www.PacktPub.com
Preface
Free Chapter
First Steps in Data Analysis
Creating an Interface for an External Program
Analyzing Data with the Help of Mathematica
Discovering the Advanced Capabilities of Time Series
Statistical Hypothesis Testing in Two Clicks
Predicting the Dataset Behavior
Rock-Paper-Scissors – Intelligent Processing of Datasets
Index

## Checking the degree of sample dependence

In statistical analysis, it is important to understand whether we are dealing with dependent or independent sets of data. This affects the system model building approach, and thus, the forecast quality.

The independence of the two data samples (represented in a vector or matrix form) is carried out with the help of the `IndependenceTest` function. This function conducts a series of tests to check the main hypothesis H0 to see whether the vectors are independent, and to check the alternative hypothesis HA to see whether the vectors are dependent.

The following tests are conducted:

Test's name

Type of test

Description

"BlomqvistBeta"

Monotonic

This is based on Blomqvist's β

"GoodmanKruskalGamma"

Monotonic, vector

This is based on the γ-coefficient

"HoeffdingD"

Vector

This is based on Hoeffding's D

"KendallTau"

Monotonic

This is based on Kendall's τ-b

"PearsonCorrelation"

Linear, normality, vector

This is based on Pearson's product-moment...