Using Statistics to Make Educational Decisions

David Tanner

• Publisher: SAGE Publications, Inc
• Year: 2011
• Print ISBN: 9781412969772
• eBook ISBN: 9781483314686
• Edition: 1
• Topic: Social Sciences
• Subtopic: Social Science Research & Methodology
• Index: Social Sciences

An accessible introduction to statistics written specifically for Education students in the changing educational landscape

Government scrutiny and intensified oversight have dramatically changed the landscape of education in recent years. Observers want to know how schools compare, which district is best, which states are spending the most per student on education, whether reforms are making a difference, and why so many students are failing. Some of these questions require technical answers that educators historically redirected to outside experts, but the questions leveled at all educators have become so acute and persistent that they can no longer be outsourced. This text helps educators develop the tools and the conceptual understanding needed to provide definitive answers to difficult statistical questions facing education today.

PART I

Developing a
Context for
Statistical Analysis

Chapter 1

A Context for Solving Quantitative Problems

Chapter 2

Describing Data

Chapter 1

A CONTEXT FOR SOLVING
QUANTITATIVE PROBLEMS

THE PROBLEM

Phil is an academic counselor at the local community college where he’s been a member of the staff for several years. He hopes one day to work in the office of institutional research, perhaps as its director. It’s been years since he took a class but he recognizes that some of the questions that he and others ask about how they’re doing at the college require some ability with quantitative analysis. He picks up a statistics text in the bookstore, leafs through the pages, and wonders whether he’s ready to pursue an advanced degree.

QUESTIONS AND ANSWERS

What does this book have to do with my career as an educator?

From kindergarteners to graduate students, today’s learners belong to the most scrutinized and indeed the most tested generation of students. Many of the questions asked about the quality of their education and about their educational progress require some quantitative analysis. This book is designed to help with just such problems.

How much of a mathematician will I need to be to navigate this textbook?

The answer is not a mathematician at all in the usual sense of that description. A little introductory algebra will help but you will need nothing beyond. It’s far more important to think logically than it is to have an extensive background in mathematics.

Since computers and software are available for statistical analysis, do I have to perform the calculations myself?

For two reasons, the answer is yes. Those who can work solutions understand the analysis more readily than those who cannot, and it’s actually quite satisfying to complete a solution longhand, although you may have to trust me on this for now.

ABOUT STATISTICS

When things are important to us, we often create a record of them. When a piece of music is particularly moving, a meal is outstanding, or a friendship is unusually meaningful, we at least create memories that serve as a more-or-less permanent record of the experience. Some of the other things that we wish to remember are important not because they involve the emotions that the foregoing evoke, but because they are a record of the choices made in the past and may become elements in the decisions that are yet to come. This seems particularly likely at a time when educators at all levels are scrutinized more carefully than perhaps they ever have been. Ours is an age of educational accountability.

Numbers offer a great economy in record keeping. Although certainly there are some things that can’t be readily reduced to numbers, this book is about describing and analyzing things that can. Some numbers are nothing more than convenient labels to indicate a category to which an individual belongs. This is the case when summaries are made of something like students’ academic majors, and for convenience, the majors are numbered. At other times, the number indicates how much of some quality an individual possesses, as with a verbal aptitude gauge where higher scores indicate that the individual measured possesses more of, or a higher level of, some characteristic than one with a lower score. In either example, the numbers allow one to reduce what could be lengthy verbal descriptions to a relatively compact record. Whether we’re gathering information about a second language speaker’s reading comprehension, the dropout rate in a particular school district, or the number of units for which entering freshman students typically register, someone is relying on their ability to quantify several important outcomes. Efforts to discover more effective teaching, curb the dropout rate, or evaluate trends in student registration often depend on educators’ abilities to manipulate and analyze quantitative data.

This is the reality that Phil faces in the chapter introduction. He, and all educators and decision makers, needs to be able to answer questions about differences and about relationships, about the way things are and how they might be improved. Questions about the average age of entering freshmen, or the changing attitudes of entering freshmen, or about whether there have been changes in students’ level of preparation for college-level study over time may involve quite intricate quantitative analyses. Equipping readers to deal with such issues is the point of this book.

REGARDING THE MATH

To be straightforward about a couple of things as we begin, note that by its nature statistical analysis is mathematical and a good deal of basic math is involved in some of the things we will do as we progress, but it is basic math. Because the issues educational decision makers face are complex and involved doesn’t always mean that the analytical techniques used to confront those issues need to be.

Does that sound inconsistent? Perhaps only continuing in the book will be convincing, but in a number of years of teaching statistical analysis, your author has come to two conclusions:

1. Students often have very little background in quantitative analysis generally, and little experience with mathematics specifically beyond an introductory algebra course.

2. The lack of mathematics needn’t be an impediment to statistical analysis and decision making.

Perhaps like the aspiring institutional researcher in the chapter introduction, that last (first?) algebra class was as long ago as somewhere in secondary school, but he, and you, can flourish nevertheless.

By the way, if the reader has more than a little algebra that’s terrific, but that hasn’t been assumed. The more advanced students among us will just need to be a little patient during the early chapters while those who have had less math, or a longer interruption, get up to speed.

If it has been a while since formal mathematics coursework, one of the more important things to do by way of beginning is just to review things like the order in which multiple mathematical operations must occur. Many of the mistakes that students make when there are multiple calculations required stem from forgetting that, in order, the student works

• in parentheses first,

• then with exponents,

• then with multiplication and division, working from left to right, doing whichever comes first, and

• then addition, and subtraction, again working the leftmost problem first.

If “please excuse my dear Aunt Sally” still helps one remember, great. If it doesn’t, find something else to use as a guide because some of the formulae involve several calculations. It’s important to be clear about whether we subtract or divide first when the formula calls for both.

For students whose earlier forays into some sort of quantitative analysis were, well, modest in outcome, a course like this can be about redemption. With some persistent study and practice, even those whose prior experiences prompt trepidation at the prospect of a statistics class can excel.

ANSWERS THE OLD-FASHIONED WAY

The truth of the matter is that in the present age, beyond balancing your checkbook (and perhaps not even that), relatively little quantitative analysis is carried out without using a computer. Sometimes there is just too much information to deal with to make avoiding the computer practical. Even when there aren’t mounds of data to absorb, computers are very convenient. Business-oriented spreadsheets such as Microsoft’s Excel, to say nothing of dedicated statistical packages like SPSS, have built-in statistical procedures that address most of the problems we’ll tackle in an introductory statistics textbook. Indeed, statistical packages provide analyses of extremely complex and involved problems. And yet there is a good deal of emphasis in this book on hand calculation...

Table of contents

• Cover
• Dedication
• Title
• Copyright
• Contents
• Detailed Contents
• Preface
• Acknowledgments
• PART I: DEVELOPING A CONTEXT FOR STATISTICAL ANALYSIS
• PART II: PRESENTING DATA
• PART III: EXAMINING DIFFERENCES
• PART IV: ASSOCIATION AND PREDICTION
• PART V: TESTS FOR NOMINAL AND ORDINAL DATA
• PART VI: TESTS, MEASUREMENT ISSUES, AND SELECTED ADVANCED TOPICS
• Glossary
• Appendices
• Index
• About the Author
• Back Matter