Fluent Essays

1.Reflection (I have no experiences on statistics) After reading Chapter 1 of the text, write a 2 page (double-spaced, 12 font) reflection paper that describes your thoughts about and experiences with statistics and the stages of the research process. 2. Assignment (You will write a paper about the use of statistics in the media, and the responsibility of the publication of statistics from research and evaluation) Read and consider Ethical Guidelines for Statistical Practice, from the American Statistical Association (PDF) and Statistics and the Media as linked in the materials. (Link: https://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/statistics/statistics-and-the-media) Write a 2 page (double-spaced) paper addressing the following questions. Be sure to use information presented in the article to support your answers. 1.Why are statistics important to share with journalists and the public? 2.How does the media often use and misuse statistics? 3.Does the information in these articles influence the way you think about your work in evaluation? Explain why or why not. Week 1 Materials How to navigate materials Each week we will cover a range of topics, readings and videos. In order to be successful, you will need to review all of the required materials. To access all materials you can use the "Table of Contents" area in the upper right corner of this screen or the "Previous" and "Next" prompts in the top and bottom corners of this section. Readings Reading Instructions Before you read, know that some of the terminology might be new to you and somewhat confusing.  We will begin to discuss this terminology in future weeks, but as you read, write down some of the technical/evaluation terms and concepts that you may not be familiar with.  Once you have read the whole case and completed your list, try to define each term briefly based on what you already know or understand.  It’s OK not to know.  It’s also OK to be ‘wrong’ as no one is going to know anyway! What this exercise might help you to figure out is just how much (or how little) you already know and understand about program evaluation.  It will also hopefully give you a sense of how large and complex and complicated some evaluations are (others are not so).  This is a case of a particular way of understanding and practicing evaluation and is grounded in a particular method of evaluation roughly defined as impact evaluation. We will cover impact evaluation, briefly, in future weeks because most impact evaluations use quantitative methods and statistics. Once you have read this case study, written down your list of terms and concepts, and briefly defined them for yourself, please answer the questions listed in the assignment.  Where possible, use the information presented in the case study to support your answers and arguments.  Your answers should be succinct but detailed enough to thoughtfully and completely answer the questions. Assignment Preparation Case Study 1：Women as Policymakers （See PDF） Course Introduction · You will also need the course text, Fundamental Statistics for the Social and Behavioral Sciences (Tokunga, 2016).  More on the text is posted below. · All other course content will be available through Moodle.   · Each week will have a Moodle lecture with required links to videos and/or external readings · After reading the weekly "lectures" (all the content in the Materials section), I recommend you do the assigned readings Textbook The text for this course is Fundamental Statistics for the Social and Behavioral Sciences by Howard T. Tokunaga, published in 2016.  Copies are available through most major online book retailers (e.g., Amazon.com).  You will be expected to have a copy of the text by the second week of the semester. Activities In addition to the weekly "lectures" and readings, you’ll also do an assignment, a quiz, and participate in either a discussion forum or write a brief reflection paper. The assignment format will vary from week to week, but each assignment will be worth the same number of points. Assignment examples include reading a case study, critiquing a journal article, or doing a problem set. You will be required to take a quiz most weeks.  Each quiz has 15 questions and is worth 15 points.  Quizzes are open book and open notes, but they are timed and you cannot discuss them with anyone in the class (before or after taking them). For half of the weeks there will be a discussion question that is posted and meant to inspire class discussion.  Active participation in each forum is expected.  For the other half of the weeks you will be required to write a brief reflection paper.  Prompts for these papers will be shared with you. Goals You will: · perform common quantitative methods and statistical techniques that are relevant to conducting an evaluation, · differentiate between the concepts of evaluation and research, and · apply their learning to the development of a quantitative evaluation project. Research and evaluation (or Program Monitoring and Evaluation, M&E) spans a wide range of conceptualizations and definitions.  Evaluators utilize a wide range of research methods and ways of thinking about and applying research, as they design and conduct evaluations.  Research methods can be either quantitative, qualitative, or a mix of both (i.e. mixed-methods).  Similarly, evaluation can be quantitative, qualitative, or mixed, and evaluations draw on these very same research methods and methodologies but they are often used by evaluators somewhat differently than researchers.  More about that in future weeks! What is important is that the methods and design that evaluators choose to use need to be relevant and appropriate to the specific program that is being evaluated and these methods need to be understood and used with the same level of insight, understanding, and rigor that formal academic researchers might do when conducting their own academic research. These first week and week 8 are designed to help explain and clarify some of the basic concepts and terminology associated with both quantitative research and evaluation. A Word About Evaluation This is not a course on evaluation, but a course on quantitative methods and statistics for use by evaluators. The course will provide a brief overview of evaluation and research. However, the main focus of the course is on the quantitative methods and statistics commonly used by evaluators. This course has been developed with the assumption that you will take additional courses focusing on 1. qualitative research methods 2. program evaluation design and methods.  You will need these things in order to become a competent evaluator! The point of departure for this course is therefore a basic understanding of evaluation (and particularly impact evaluation).  You also need a basic understanding of, and skill in, math. A Word about Math Calculators are encouraged. You don’t need to be the hero who does hand calculations! If you know how to add, subtract, multiply, and divide, you’re in good shape. You’ll need to know some basic Algebra. In algebra, numbers are often represented as symbols called variables (e.g., x, n, y, or z). You will need to solve for variables like you do in the equation below. x + 50 = 150 (x = 100) You’ll also need to know these... 1. Powers 2. Coefficients  3. Groupings 4. Operators 5. Constants Need to brush up on your Algebra? （Link） · Khan Academy · Cool Math See where your basic math skills are by taking this week's Moodle quiz. This is a graded and required quiz. 1 Running head: EXPLORING THE EFFECT OF WOMEN IN GOV. IN INDIA 2 EXPLORING THE EFFECT OF WOMEN IN GOV. IN INDIA Exploring the Effect of Women in Government in India Wenye Liang Quantitative Methods and Statistics for Evaluators Nicole Gilbert Cote 05/23/2020 Exploring the Effect of Women in Government in India The federal constitution of India was amended in 1992 to devolve power. The local government was brought into the forefront in determining administration at the village levels (Abdul Latif Jameel Poverty Action Lab, n.d). These administrative units are governed by the village councils (gram panchayats), that prepare the budget and choose the development programs that need to be implemented. The constitutional amendment also provided for women engagement in leadership and policymaking. All states are required to reserve a third of all council seats for women in a rotational allotment. Despite this constitutional requirement, the quota system has only achieved marginal success, with India recording 10 percent of women in government compared with the global average of 17 percent. In evaluating the matter from a research perspective, the proposed study would be guided by the overarching question: to what extent has the constitutional women representation quota in India affected representative policymaking in the country? By answering this question, the research would evaluate the developmental impact of the quota system in India’s grassroots by comparing development in areas with relatively higher women representation in areas with little to no women representation. The research would create valuable knowledge that determines the impact of women in leadership on grassroots development and understands the significance of the 1992 constitution amendment of India towards the representation of women in policymaking. To perform this research, the researcher would require information on the number of women in leadership across different localities in India and development statistics or reports for those areas. This report would be dependent on the availability of development reporting in India’s grassroots as well as historical records of women representation since the enactment of the 73rd Amendment. Depending on the availability of data, a suitable research design would be selected. To provide a representative sample, the researcher may consider selecting several regions that provide both rural and urban localities. Local councils could represent several villages. Selecting a sample that represents the average local council in India would be suitable for the research, thus keeping the size and scope of the research manageable. At least ten villages could be selected to provide baseline characteristics. This research should incorporate a mixed-methods design. Mixed-methods designs are conventionally used to evaluate complex interventions, such as gender quotas in governments that are implemented differently across different regions (Capstick & Pidgeon, 2014). The effect of women in governance is a complex phenomenon since it is dependent on multiple social, political, and economic factors for its implementation. The researcher may apply a convergent approach, allowing the study to review both quantitative and qualitative resources (Capstick & Pidgeon, 2014). In this way, the researcher could gather data from women in government. They will be asked about the timeline for their political careers, investments in public goods, education levels, and political experiences. The researcher would assess public reports that measure the implementation of gender quotas. These sources could validate each other and provide the research with a strong foundation for reaching conclusions regarding gender policy. The researcher would collect the number of female representatives (quantitative data) and descriptions and highlights of the gender quota policy (qualitative data) for analysis, and then demonstrate the success of the gender quota policy in village-level development. The findings would present gender quota differences across different regions and compare development outcomes in those regions. Items such as gender representation, literacy levels, quality of public infrastructures such as healthcare, schools, and roads would be considered. In effect, the outcomes of the research will evaluate whether gender representation in grassroots leadership influences the quality of life for constituents. The findings would then be presented using both graphical and tabular results. Graphical results enable the audience to quickly and summarily understand the effect of women in government, while the tabular results could present the extensive results of the proposed study through the various data analysis methods applied. Alternatively, the proposed study could provide an executive summary that captures its main findings. The potential clients for this research are policymakers at the federal government of India and the local governments (Panchayat Directorates) who may be interested in establishing if it has achieved its goal of increasing the participation of women in politics and understanding the effect of (greater) gender representation at the government by assessing the current effects of this legislation. The stakeholders are political leaders, special interest groups like women rights activists, and the public. Finally, the research is expected to take at least two years. This time will be sufficient to plan for the study, recruit the required teams, pilot test, collect data, and analyze the findings. Most of time would be appropriate for reconnaissance studies into the dynamics of local government leadership in India’s rural areas. The researcher need time to familiarize themselves with the recordkeeping techniques that this leadership structures keep, thereby determining how the mixed-methods approach will best be applied. Based on these factors and the fact that the total budget of the research is estimated at $28,000. The fixed costs will be $16,000 and cater for the enumeration of the research teams, equipment, and services such as data storage and publication costs. The indirect cost will amount to $12,000 and cater to consultation costs, office supplies, and travel expenditures. References Abdul Latif Jameel Poverty Action Lab. (n.d). Case study 1: Women as policy makers. Capstick, S. B., & Pidgeon, N. F. (2014). What is climate change skepticism? Examination of the concept using a mixed-methods study of the UK public. Global Environmental Change, 24, 389-401. Fundamental Statistics for the Social and Behavioral Sciences 2 To my kids, Meagan and Will, and my parents, Katsumi and Grayce Tokunaga. 3 Fundamental Statistics for the Social and Behavioral Sciences Howard T. Tokunaga San Jose State University 4 FOR INFORMATION: SAGE Publications, inc. 2455 Teller Road Thousand Oaks, California 91320 E-mail: [email protected] SAGE Publications Ltd. 1 Oliver's Yard 55 City Road London EC1Y 1SP United Kingdom SAGE Publications India Pvt. Ltd. B 1/I 1 Mohan Cooperative Industrial Area Mathura Road, New Delhi 110 044 India SAGE Publications Asia-Pacific Pte. Ltd. 3 Church Street #10-04 Samsung Hub Singapore 049483 Copyright © 2016 by SAGE Publications, Inc. All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All trademarks depicted within this book, including trademarks appearing as part of a screenshot, figure, or other image are included solely for the purpose of illustration and are the property of their respective holders. The use of the trademarks in no way indicates any relationship with, or endorsement by, the holders of said trademarks. SPSS is a registered trademark of International Business Machines Incorporated. Printed in the United States of America Cataloging-in-Publication Data is available for this title from the Library of Congress. ISBN 978-1-4833-1879-0 5 This book is printed on acid-free paper. 15 16 17 18 19 10 9 8 7 6 5 4 3 2 1 Acquisitions Editor: Vicki Knight Editorial Assistant: Yvonne McDuffee Associate Editor: Katie Bierach Production Editor: Kelly DeRosa Copy Editor: Gillian Dickens Typesetter: C&M Digitals (P) Ltd. Proofreader: Jennifer Grubba Indexer: Marilyn Augst Cover Designer: Candice Harman Marketing Manager: Nicole Elliott 6 Detailed Contents Preface Acknowledgments About the Author Chapter 1. Introduction to Statistics Chapter 2. Examining Data: Tables and Figures Chapter 3. Measures of Central Tendency Chapter 4. Measures of Variability Chapter 5. Normal Distributions Chapter 6. Probability and Introduction to Hypothesis Testing Chapter 7. Testing One Sample Mean Chapter 8. Estimating the Mean of a Population Chapter 9. Testing the Difference between Two Means Chapter 10. Errors in Hypothesis Testing, Statistical Power, and Effect Size Chapter 11. One-Way Analysis of Variance (ANOVA) Chapter 12. Two-Way Analysis of Variance (ANOVA) Chapter 13. Correlation and Linear Regression Chapter 14. Chi-Square Tables Appendix: Review of Basic Mathematics Glossary References Index 7 Preface It may surprise students to learn they have something in common with writers of books such as this one: When you get close to finishing a writing assignment, you get a bit tired and a bit lazy. The first attempt at this preface was written shortly after final drafts of chapters were sent to my editor at SAGE, Vicki Knight. After reading it, she said, “It's not bad, but it reads like the ‘typical’ Preface. I think it would be useful for the reader to have a sense of why you wrote this book and why you wrote it the way you did.” In responding to my editor's plea for self-analysis, I found that this book's journey began in college. When I entered college, I thought my path would take me to law school; however, taking an Intro to Psych class my freshman year made me realize I enjoy the challenge of trying to understand the human mind. The school I attended, UC Santa Cruz, was a fairly unconventional university, but somehow in the midst of a sea of humanistic psychologists, I became attracted to the empirical and methodological aspects of psychology. This was a result of taking classes with instructors such as David Harrington and Dane Archer, who showed me that statistics could appeal to students if taught using a gentle, guiding approach that addresses questions relevant to students' lives. After graduating from college, I was able to get a job as a research assistant for a human resource consulting firm. Despite my lack of work experience, I was hired primarily as a result of having taken statistics and research methods courses, which taught me that learning statistics has benefits both inside and outside of the classroom. Several years later, I started grad school at UC Berkeley, where two events critical to this book took place. First, serving as a teaching assistant, I found I really enjoyed helping students, particularly in statistics and research methods classes that were often viewed with fear and suspicion. Second, I took graduate classes from Geoff Keppel, who had developed his own unique method and system for analyzing experimental research designs. His lectures and books were instrumental in showing me that statistics can be taught in a systematic way that highlights similarities rather than differences between different research situations. Geoff managed to transform something as daunting sounding as a “3 × 2 × 4 research design” into the mathematical equivalent of playing with wooden toy alphabet blocks labeled “A,” “B,” and “C.” For a long time, I thought my gratitude to Geoff was an isolated occurrence. However, the appreciation others have for his approach to teaching statistics was made apparent to me several years later when I watched him receive an American Psychological Association (APA) Lifetime Achievement award. After leaving Cal, I took on a teaching position at San Jose State, where my teaching responsibilities included an introductory statistics course aimed at students with a wide range of background, ability, and motivation. As I needed to select a textbook to use in this course, for the first time I looked carefully at the wide range of offerings. What I found 8 striking (and still find striking) was that the majority of books focused on providing formulas and very small sets of data designed to demonstrate how to correctly calculate the correct numbers from these formulas. Little emphasis, however, was given to what these numbers meant or implied. Given my own experiences learning statistics, I thought a book was needed that discusses statistics in a thematic manner, focusing on how they are used to answer questions and test ideas within the larger research process. The primary purpose of this book is to not just teach students how to calculate statistics but how to interpret the results of statistical analyses in light of a study's research hypothesis and to communicate one's results and interpretations to a broader audience. Hopefully, this book will not only help students understand the purpose and use of statistics but also give them a greater understanding of how research studies are conceived, conducted, and communicated. The 14 chapters of this book may be placed into three general categories. The first four chapters are designed to introduce students to the research process and how data that have been collected may be organized, presented, and summarized. Chapters 5 through 10 discuss the process of conducting statistical analyses to test research questions and hypotheses, as well as issues and controversies regarding this process. The final four chapters of this book, Chapters 11 to 14, discuss different statistical procedures used in research situations that vary in the number of independent variables in the study as well as how the independent and dependent variables have been measured. 9 A Few Tips for Students To you, the college student about to read this book as part of taking a statistics course: “Welcome!” and “Great job!” I welcome you because you're about to embark on a semester-long journey that I hope will enhance your skills and widen your perspective; I congratulate you because it's a journey not everyone is willing to take. At the present moment, I know my encouragement and appreciation may be of little comfort to you as you might be somewhat anxious about having to learn statistics. Some of you might be anxious about having to learn statistical concepts and formulas; some of you might be anxious because the research process seems pretty complicated. Talking with students who have taken my courses over the years has helped me assemble the following advice: 10 Master the Material Presented in the Early Chapters Chapters 1 through 6 discuss how research is often conducted, how data are summarized and described, and the process by which researchers conduct statistical analyses to test their ideas. It is absolutely critical for you to have a firm understanding of these chapters as they lay the groundwork for later chapters that discuss a variety of statistical procedures used by researchers to test hypotheses. What does it mean to master this material? First, read the chapters both before and after they're discussed in class. By reading the chapters beforehand, you'll be able to identify anything that's unclear to you and have your questions addressed by your instructor. Rereading the chapters after they're discussed in class will help confirm your understanding of the material. Next, be able to define and explain key concepts presented in these chapters. These concepts are highlighted in bold-faced type, and it is important to learn them when they're first introduced because they'll appear throughout the remainder of the book. Next, do the learning checks within the chapters and the exercises at the end of the chapters. The learning checks include both exercises and review questions you can ask yourself to assess your understanding of the material. Most important, do not miss class during the early part of the semester! It's been my experience that students who miss critical lectures at the beginning of the term often have difficulty keeping up as the semester continues. 11 Review High School Algebra If you read newspapers or watch television, you might conclude that the most complicated data analysis people can comprehend is a pie chart. As frustrating as this is to researchers and statistics instructors, they understand that statistics can be confusing. If you happen to move beyond the introductory statistics course for which you are reading this book, you'll find that statistical procedures are often conducted using computers and statistical software rather than hand calculations. Consequently, some statistics textbooks no longer include mathematical formulas but instead have students conduct analyses using statistical software or Microsoft Excel. However, this book has chosen a different approach for two main reasons. First, I believe that to comprehend the results of data analysis, one must understand the underlying foundation of statistical procedures. Learning statistics via computer software can lead to a “brain-dead” approach in which students are at the mercy (rather than control) of their computers. I refer to this as the “I'm only as smart as my printout” method of learning statistics, also known as “Because this is what my computer told me.” Second, my steadfast and somewhat stubborn adherence to an approach emphasizing mathematical formulas and calculations is based on a simple reason: The statistics in this book are not hard to calculate! To assess whether you're adequately prepared to read this book, take the following test: 1. Do you know how to add, subtract, multiply, and divide? 2. Do you know how to calculate the “square” or “square root” of a number? 3. Do you understand the “order of operations” and how to use parentheses within mathematical calculations? If your answers to these questions are yes, congratulations! You possess the ability to conduct every mathematical calculation in this book. None of the formulas in this book requires knowledge of geometry, trigonometry, or calculus. However, if you're unsure of your mathematical ability, you may want to review your high school algebra. At the end of this book is an appendix that includes the mathematical concepts and operations needed to conduct the statistical analyses in this book. I highly recommend you read this appendix to review and assess your mathematical skills. 12 Learn to Use a Statistical Calculator Although learning the statistics in this book doesn't require the use of computers or software, you will need a hand calculator. Calculators with statistical capabilities are typically identified as statistical or scientific calculators. Although there's a wide selection of brands and models, one simple criterion to use in selecting a calculator is price. The statistical calculators most appropriate for this book cost somewhere in the $10 to $15 range at the time of this writing. I do not recommend you use or purchase a more expensive calculator! I prefer these simpler calculators because I've found students are able to conduct the calculations in this book more quickly and with fewer errors. I also recommend you purchase a calculator similar to the one your instructor uses as he or she will be more familiar with its features and idiosyncrasies. In selecting a calculator, look closely at the keyboard; you'll need a calculator whose keys have labels such as “ X ¯ ,” “σ,” and “ΣX” (Chapters 3 and 4 discuss what these symbols represent). When you go calculator shopping, you'll find calculators that have keys with labels such as “ΣY” and “XY.” Although calculators with these “Y” symbols are only slightly more expensive than calculators with just the “X” symbols, I do not recommend their purchase because these features are not needed to perform the calculations in this book. In fact, I've found students with “Y” calculators have a more difficult time performing simpler calculations. 13 Ask Questions Conducting research is the process of asking and answering questions. Accordingly, throughout this book, issues are often framed in the form of questions, which I hope encourages you to ask questions as well. The first person you should direct any questions to is yourself. As you work your way through the chapters, get into the habit of asking yourself, “What does this mean?” A good test of your level of comprehension is whether you can explain the material to yourself in a meaningful way. Also, be sure to work with your instructor to confirm your level of understanding and clarify unanswered questions. Instructors often say to students, “The only ‘bad’ question is the one you don't ask.” Don't be hesitant about asking questions in class. Instructors will tell you they use one student's question to assess an entire class' level of understanding. This is what I call the “pencil test”—when one student asks a question, I look to see how many other pencils get raised, which reflects the number of students who had the same question and are ready to write down the response. Asking questions enhances the learning experience for yourself, your classmates, and your instructor. 14 Form a Study Group No matter how much I encourage students to ask questions in class, it seems they hesitate for fear of drawing attention to themselves. As a result, I turn to another well-traveled saying: “Misery loves company.” Forming a study group to meet with other students on a regular basis will help you keep up with reading assignments, confirm your comprehension of the material, clarify any confusion you have, prepare for exams, and receive an invaluable source of social support. I do suggest that your group contain at least one person who will raise the group's questions and concerns to the instructor in class or office hours. 15 Practice, Practice, Practice The best way to learn the topics covered by this book is to obtain as much practice as possible. Throughout the chapters are examples in which the calculations have been worked out for you; in the middle and end of each chapter are a number of exercises. The answers to some of the exercises are provided at the back of this book, and your instructor has access to the answers to the other exercises. Do the end-of-chapter exercises even if your instructor does not assign them as homework in order to identify any recurring mistakes you make. We find that the vast majority of errors students make are simple computational errors, committed when students do the calculations too quickly. WELCOME! GREAT JOB! 16 Acknowledgments This book has traveled a long journey, with many people playing both transient and persevering roles in its development. First and foremost, I'd like to thank my kids, Meagan and Will, for providing me perspective and inspiration amid all of the twists and turns we faced while this book was being written. I'm so very blessed to have you as my “burden.” Away from home, I'm grateful to my graduate students at San Jose State—working on this book has given me much empathy for their thesis-related travails. However, they should be aware that the completion of this book ends the unspoken agreement that I not ask, “So how's your thesis?” if they don't ask, “So how's your book?” A number of friends have provided most welcome relief after long days staring at a computer screen, with particular thanks going to Ellie, Eileen, Susan, Bonnie, Ann, Lisa, and Terry. I would like to thank Charles Linsmeier and David Shirley for their many helpful comments and advice on earlier versions of this book, and Julie West for her help in developing chapter exercises. I would like to express my appreciation to everyone at SAGE who has played a role in shepherding this book to completion. First and foremost, I must express my gratitude to my editor, Vicki Knight. It has been a joy and an honor to work with someone with such a truly exceptional combination of experience, knowledge, perspective, and humor. In production I was fortunate enough to work with others on the SAGE team who made the process a pleasure: Yvonne McDuffee, Editorial Assistant; Katie Guarino, Assistant Editor; Nicole Elliott, Executive Marketing Manager; Candice Harman, Cover Designer; and the copyeditor, Gillian Dickens. Furthermore, I am grateful to the reviewers, who took the time to read the chapters, raise questions, and provide constructive comments and suggestions to assist me in clarifying and strengthening the manuscript: Holly R. Straub, The University of South Dakota Shelly A. McGrath, University of Alabama at Birmingham Jim Allen, State University of New York, Geneseo David Schuster, San José State University Hideki Morooka, Fayetteville State University Andrea J. Sell, California Lutheran University Christine D. MacDonald, Indiana State University Robert G. LaChausse, California State University, San Bernardino 17 Melissa J Beers, Ohio State University 18 About the Author Howard T. Tokunaga is Professor of Psychology at San Jose State University, where he serves as Coordinator of the MS Program in Industrial/Organizational (I/O) Psychology and teaches undergraduate and graduate courses in statistics, research methods, and I/O psychology. He received his bachelor's degree in psychology at UC Santa Cruz and his PhD in psychology at UC Berkeley. In addition to his teaching, he has consulted with a number of public-sector and private-sector organizations on a wide variety of management and human resource issues. He is coauthor (with G. Keppel) of Introduction to Design and Analysis: A Student's Handbook. 19 Chapter 1 Introduction to Statistics 20 Chapter Outline 1.1 What Is Statistics? 1.2 Why Learn Statistics? 1.3 Introduction to the Stages of the Research Process Developing a research hypothesis to be tested Identifying a question or issue to be examined Reviewing and evaluating relevant theories and research Stating a research hypothesis: Independent and dependent variables Collecting data Drawing a sample from a population Determining how variables will be measured: Levels of measurement Selecting a method to collect the data: Experimental and non-experimental research methods Analyzing the data Calculating descriptive statistics Calculating inferential statistics Drawing a conclusion regarding the research hypothesis Communicating the findings of the study 1.4 Plan of the Book 1.5 Looking Ahead 1.6 Summary 1.7 Important Terms 1.8 Exercises In introducing this book to you, we assume you are a college student who is taking what is perhaps your first course in statistics to fulfill a requirement for your major or a general education requirement. If so, you may be asking yourself two questions: What is statistics? Why learn statistics? The ultimate goal of this book is to help you begin to answer these two questions. 21 1.1 What is Statistics? Whether or not you are aware of it, you encounter a variety of “statistics” in your day-to- day activities: the typical cost of going to college, the yearly income of the average college graduate, the average price of a home, and so on. So what exactly is “statistics”? The Merriam-Webster dictionary defines statistics as a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. When people think about statistics, they often focus on only the “analysis” aspect of the above definition—that is to say, they focus on numbers that result from analyzing data. However, statistics is not only concerned about how data are analyzed, it recognizes the importance of understanding how data are collected and how the results of analyses are interpreted and communicated. The purpose of this book is to introduce, describe, and illustrate the role of statistics within the larger research process. 22 1.2 Why Learn Statistics? We believe there are a variety of reasons why you should learn statistics. First, not only do you currently encounter statistics in your daily activities, but throughout your life, you have been and will continue to be affected by the results of research and statistical analyses. Which college or graduate school you attend is based in part on test scores developed by psychologists. You may also have to take a personality or intelligence test to get a job. The choices of drugs and medicines available to you are based on medical research and statistical analyses. If you have children, their education may be affected by their scores on achievement or aptitude tests. Learning about statistics will help you become a more informed and aware consumer of research and statistical analyses that affect many aspects of your life. A second reason for learning statistics is that you may be asked or required to read and interpret the results of statistical analyses. Many college courses require students to read academic research journal articles. Evaluating published research is complicated by the fact that different people studying the same topic may come up with diverse or even opposing conclusions. Understanding statistics and their role in the research process will help you decide whether conclusions drawn in research articles are appropriate and justified. Another reason for learning statistics is that it will be of use to you in your own research. College courses sometimes have students design and conduct mini-research studies; undergraduate majors might require or encourage students to do senior honors theses; graduate research programs often require masters' theses and doctoral dissertations. Learning to collect and analyze data will help you address your own questions in an objective, systematic manner. A final reason for learning statistics is that it may help you in your future career. The website Careercast.com conducts an annual survey in which they evaluate 200 professions on five dimensions: environment, income, employment outlook, physical demands, and stress. In 2013, the highest rated profession in this survey was “actuary,” defined as someone who “interprets statistics to determine probabilities of accidents, sickness, and death, and loss of property from theft and natural disasters.” Talking about his job, one actuary noted, “I can count on one hand the number of days I've said, ‘I don't want to go to work today’ … I've seen people come in to say thank you for the work I've done. That's pretty powerful.” It is generally a good idea for students to maintain a healthy level of curiosity or even skepticism in regards to their education. However, we find that when it comes to learning statistics, the frame of mind of some students may be characterized as one of fear and anxiety. Although we understand these feelings, we hope the benefits associated with learning statistics will become clear to you and help you overcome any concerns you may 23 have. 24 1.3 Introduction to the Stages of the Research Process Much of scientific research involves asking questions. Throughout this book, we will examine how contemporary researchers have asked and attempted to answer a broad range of questions regarding human attitudes and behavior. Below are research questions we will address in this chapter to introduce the stages of the research process: Is students' performance on tests more influenced by their learning strategies (how they learn) or their motivation (why they learn)? Do college students and faculty differ in their beliefs about the prevalence of student academic misconduct such as cheating and plagiarism? Is the extent to which adolescents are exposed to violence in their community related to how they do in school? Is one method of disciplining ones children more effective than another? Does playing online computer games affect ones interpersonal relationships? Does providing substance abuse treatment to drug users have an effect on safety in the workplace? How might you try to answer questions such as these? You could base your answers on your personal beliefs, or you could adopt the answers given to you by others. But rather than relying on subjective beliefs and feelings, researchers test their ideas using science and the scientific method. The scientific method is a method of investigation that uses the objective and systematic collection and analysis of empirical data to test theories and hypotheses. At its simplest, this book will portray the scientific method as consisting of five main steps or phases: developing a research hypothesis to be tested, collecting data, analyzing the data, drawing a conclusion regarding the research hypothesis, and communicating the findings of the study. Accomplishing each of these five steps requires completing a number of tasks, as shown in Figure 1.1. Because this sequence of steps will be used throughout this book and will serve as the model for the wide assortment of research studies we will review and discuss, each step is briefly introduced below. It is important to understand that the research process depicted in Figure 1.1 represents an ideal way of doing research. The “real” way, as you may discover in your own efforts or from speaking with researchers, is often anything but a smooth ride but rather is filled with starts and stops, dead ends, and wrong turns. 25 Developing a Research Hypothesis to be Tested The initial stage—and the first step—of the research process is to develop a research hypothesis to be tested. A research hypothesis is a statement regarding an expected or predicted relationship between variables. A variable is a property or characteristic of an object, event, or person that can take on different values. One example of a variable is “U.S. state,” a variable with 50 possible values (Alabama, Arkansas, etc.). Figure 1.1 Steps in the Research Process within the Scientific Method Research hypotheses are usually developed through the completion of several tasks: identifying a question or issue to be examined, reviewing and evaluating relevant theories and research, and stating a research hypothesis. Each of these three tasks is described below. Identifying a Question or Issue to be Examined Most research starts with a question posed by the researcher. These questions often come 26 from the researchers own ideas and daily observations. Although this may not seem terribly scientific, there is an advantage in using one's own experience as a starting point: People are generally much more motivated to explore a question or topic that concerns them personally. In teaching statistics, we frequently advise students developing their own research projects to study something that is of interest to them. Conducting research can be tedious, difficult, and frustrating. At various points during your research, you may ask yourself, “Why am I doing this?” Being able to provide a satisfactory answer to this question will help you overcome whatever obstacles you encounter along the way. Reviewing and Evaluating Relevant Theories and Research Beyond the researcher's own curiosity, research questions often arise from an examination of the theories, ideas, and research of others. A theory is a set of …