Jim Frost - IntroStatisticsIntuitiveGuide

Introduction to Statistics

An Intuitive Guide For Analyzing Data and Unlocking Discoveries

Jim Frost

Statistics By Jim Publishing

STATE COLLEGE, PENNSYLVANIA

U.S.A.

Copyright 2019 by Jim Frost.

All rights reserved. No part of this publication may be reproduced, distributed or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law.

Published by: Statistics By Jim Publishing

State College, PA 16801

To contact the author, please email: jim@statisticsbyjim.com.

Visit the authors website at statisticsbyjim.com .

Ordering Information: Quantity sales. Special discounts are available on quantity purchases by educators. For details, contact the email address above.

Introduction to Statistics: An Intuitive Guide for Analyzing Data and Unlocking Discoveries/ Jim Frost. 1st ed.

ISBN 978-1-7354311-3-0 (EPUB)

Contents

Introduction

Prepare for an Adventure!

I love statistics and analyzing data! I also love talking and writing about it. I was a researcher at a major university. Then, I spent over a decade working at a major statistical software company. During my time at the software company, I learned how to present statistics in a manner that makes it more intuitive. I want you to understand the essential concepts, practices, and knowledge for statistics so you can analyze your data confidently. Thats the goal of my book.

Over the years, I've literally received thousands of requests from aspiring data scientists for statistical guidance. This book is my answer - years of knowledge and thousands of hours of hard work distilled into a thorough, practical guide for understanding statistics.

I hope this book helps you see statistics through my eyes as a key that can unlock discoveries trapped in your data. Discovery is a bumpy road. There might be statistical challenges en route, but they can be exciting and rewarding to resolve. Sometimes it is the perplexing mystery in your data that prompts you to play detective and leads you to surprising discoveries!

I hope youll view this book as a voyage. We start with the practical nuts and bolts about the field of statistics and data analysis. Then we move to the broader context of the process and challenges of using statistics to expand human knowledge. Now, thats an adventure in statistics!

In this book, you'll learn about the many facets of the field of statistics. Well start with an overview of statistics and why it is so important. Then, we move on to the necessary skills and knowledge about the different types of data, and how to summarize data both graphically and numerically. Importantly, Ill show you how to discover relationships between your variables. After that, we go to the next level and learn about populations and how to estimate their properties using samples.

Finally, we look at how statistics are part of the scientific method and help expand the scope of human knowledge. This process includes designing experiments that identify causation, rather than mere correlation, by accounting for challenges that all studies face. The book closes with criteria you can use to evaluate the quality of both the data and the design of the experiment itself. These criteria are useful for critiquing your research or other researchers' experiments.

Reading this book will allow you to take your skills to the next level. Youll be able to proceed onto more advanced statistical studies such as hypothesis testing, regression analysis, and experimental design. Alternatively, youll have a solid foundation for a career in data science and machine learning.

Youll notice that there are not many equations in this book. After all, you should let your statistical software handle the calculations while you instead focus on understanding your results. Consequently, I focus on the concepts and practices that youll need to know to perform the analysis and interpret the results correctly. Ill use more graphs than equations! If you need the equations, youll find them in most textbooks.

Please note that throughout this book I use Minitab statistical software. However, this book is not about teaching particular software but rather how to perform basic graphing and analysis. All common statistical software packages should be able to perform the analyses that I show. There is nothing in here that is unique to Minitab.

Throughout this book, I include links to download datasets from my website so you can learn by doing. You can also download them from:

https://statisticsbyjim.com/introductionstatistics

CHAPTER 1

The Importance of Statistics

Statistics are everywhere today. Youll run across them in your everyday life. Four of five dentists prefer this toothpaste! On the news. This scientific poll used random sampling and has a margin of error of 3%. In school. Your grades were averages of scores. Perhaps you were graded on a curve? Then, you took the SAT, ACT, or GRE and received your results with percentiles. Youll find statistics in almost every aspect of life: Nielsen TV ratings, surveys, political polls, insurance rates, and so on. And then, of course, there are the ubiquitous sports statistics, batting averages, third-down conversions, and countless more! Politicians and policy wonks use statistics to make their cases. Companies use statistics to use data to make decisions and increase their profits.

The field of statistics is crucial for expanding scientific knowledge. Statistical analyses are present in virtually every scientific study. Indeed, these analyses determine whether the results of the study are significant and worthy of being published. Its powerful stuff. But what is the field of statistics exactly?

The field of statistics is the science of learning from data. Statistical knowledge helps you use the proper methods to collect the data, employ the correct analyses, and effectively present the results. Statistics is a crucial process behind how we make discoveries in science, make decisions based on data, and make predictions. Statistics allows you to understand a subject much more deeply. Surprisingly, the field isnt only about numeric results. It also involves a wide range of practices, decisions, and methodologies for both collecting data and analyzing them in a manner that produces valid findings and sound conclusions.

Lets start by covering two main reasons why studying the field of statistics is crucial in modern society. First, statisticians are guides for learning from data and navigating common problems that can lead you to incorrect conclusions. Second, given the growing importance of decisions and opinions based on data, its crucial that you can critically assess the quality of analyses that others present to you.

In my view, statistics is an exciting field about the thrill of discovery, learning, and challenging your assumptions. Statistics facilitates the creation of new knowledge. Bit by bit, we push back the frontier of what is known.

Draw Valid Conclusions

Statistics are not just numbers and facts. You know, things like 4 out of 5 dentists prefer a specific toothpaste. Instead, its an array of knowledge and procedures that allow you to learn from data reliably. Statistics enable you to evaluate claims based on quantitative evidence and help you differentiate between reasonable and dubious conclusions. That aspect is particularly vital these days because data are so plentiful along with interpretations presented by people with an agenda.