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An Introduction to Psychological Statistics Garett .C Foster University of Missouri-St University of Missouri, St. Louis IRL @ UMSL Open Educational Resources Collection Open Educational Resources 11-13-2018 An Introduction to Psychological Statistics Garett .C Foster University of Missouri-St. Louis, [email protected] David Lane Rice University, [email protected] David Scott Rice University Mikki Hebl Rice University Rudy Guerra Rice University See next page for additional authors Follow this and additional works at: https://irl.umsl.edu/oer Part of the Applied Statistics Commons, Mathematics Commons, and the Psychology Commons Recommended Citation Foster, Garett .;C Lane, David; Scott, David; Hebl, Mikki; Guerra, Rudy; Osherson, Dan; and Zimmer, Heidi, "An Introduction to Psychological Statistics" (2018). Open Educational Resources Collection. 4. https://irl.umsl.edu/oer/4 This Textbook is brought to you for free and open access by the Open Educational Resources at IRL @ UMSL. It has been accepted for inclusion in Open Educational Resources Collection by an authorized administrator of IRL @ UMSL. For more information, please contact [email protected]. Authors Garett .C Foster, David Lane, David Scott, Mikki Hebl, Rudy Guerra, Dan Osherson, and Heidi Zimmer This textbook is available at IRL @ UMSL: https://irl.umsl.edu/oer/4 AN INTRODUCTION TO PSYCHOLOGICAL STATISTICS Department of Psychological Sciences University of Missouri – St Louis This work was created as part of the University of Missouri’s Affordable and Open Access Educational Resources Initiative (https://www.umsystem.edu/ums/aa/oer). The contents of this work have been adapted from the following Open Access Resources: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Changes to the original works were made by Dr. Garett C. Foster in the Department of Psychological Sciences to tailor the text to fit the needs of the introductory statistics course for psychology majors at the University of Missouri – St. Louis. Materials from the original sources have been combined, reorganized, and added to by the current author, and any conceptual, mathematical, or typographical errors are the responsibility of the current author. This work is licensed under a Creative Commons Attribution-NonCommercial- ShareAlike 4.0 International License. pg. 1 Prologue: A letter to my students Dear Students: I get it. Please believe me when I say that I completely understand, from firsthand experience, that statistics is rough. I was forced to take an introductory statistics course as part of my education, and I went in to it with dread. To be honest, for that first semester, I hated statistics. I was fortunate enough to have a wonderful professor who was knowledgeable and passionate about the subject. Nevertheless, I didn’t understand what was going on, why I was required to take the course, or why any of it mattered to my major or my life. Now, almost ten years later, I am deeply in love with statistics. Once I understood the logic behind statistics (and I promise, it is there, even if you don’t see it at first), everything became crystal clear. More importantly, it enabled me to use that same logic not on numerical data but in my everyday life. We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness. I understand that this is a foreign language to most people, and it was for me as well. I also understand that it can quickly become esoteric, complicated, and overwhelming. I encourage you to persist. Eventually, a lightbulb will turn on, and your life will be illuminated in a way it never has before. I say all this to communicate to you that I am on your side. I have been in your seat, and I have agonized over these same concepts. Everything in this text has been put together in a way to convey not just formulae for manipulating numbers but to make connections across different chapters, topics, and methods, to demonstrate that it is all useful and important. So I say again: I get it. I am on your side, and together, we will learn to do some amazing things. Garett C. Foster, Ph.D. pg. 2 Table of Contents Prologue: A letter to my students ............................................................................................... 2 Chapter 1: Introduction ............................................................................................................... 8 What are statistics? ................................................................................................................... 8 Why do we study statistics? ................................................................................................... 10 Types of Data and How to Collect Them ............................................................................ 11 Collecting Data ....................................................................................................................... 19 Type of Research Designs ...................................................................................................... 24 Types of Statistical Analyses .................................................................................................. 26 Mathematical Notation ......................................................................................................... 32 Exercises – Ch. 1 ...................................................................................................................... 34 Answers to Odd-Numbered Exercises – Ch. 1 .................................................................... 35 Chapter 2: Describing Data using Distributions and Graphs ................................................ 36 Graphing Qualitative Variables ............................................................................................ 36 Graphing Quantitative Variables ......................................................................................... 43 Exercises – Ch. 2 ...................................................................................................................... 69 Answers to Odd-Numbered Exercises – Ch. 2 .................................................................... 72 Chapter 3: Measures of Central Tendency and Spread ...................................................... 73 What is Central Tendency? ................................................................................................... 73 Measures of Central Tendency ............................................................................................. 79 Spread and Variability ........................................................................................................... 85 Exercises – Ch. 3 ...................................................................................................................... 93 Answers to Odd-Numbered Exercises – Ch. 3 .................................................................... 94 Chapter 4: z-scores and the Standard Normal Distribution .................................................. 95 Normal Distributions ................................................................................................................ 95 z-scores ..................................................................................................................................... 96 Z-scores and the Area under the Curve ............................................................................ 101 Exercises – Ch. 4 .................................................................................................................... 102 Answers to Odd-Numbered Exercises – Ch. 4 .................................................................. 103 Chapter 5: Probability .............................................................................................................. 105 What is probability? .............................................................................................................. 105 Probability in Graphs and Distributions .............................................................................. 107 pg. 3 Probability: The Bigger Picture............................................................................................. 114 Exercises – Ch. 5 .................................................................................................................... 114 Answers to Odd-Numbered Exercises – Ch. 5 .................................................................. 115 Chapter 6: Sampling Distributions .......................................................................................... 116 People, Samples, and Populations ..................................................................................... 116 The Sampling Distribution of Sample Means ..................................................................... 117 Using Standard Error for Probability .................................................................................... 121 Sampling Distribution, Probability and Inference ............................................................. 124 Exercises – Ch. 6 .................................................................................................................... 124 Answers to Odd-Numbered Exercises
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