Introductory Statistics: Concepts, Models, and Applications
David W. Stockburger
This course is designed for individuals who desire knowledge about some very important tools used by the Behavioral Sciences to understand the world. Some degree of mathematical sophistication is necessary to understand the material in this course. The prerequisite for Psy 200 is a first course in Algebra, preferably at the college level. Students have succeeded with less, but it requires a greater than average amount of time and effort on the part of the student. If there is any doubt about whether or not you should be in the course, it is recommended that the chapter on the Review of Algebra be attempted. If successful, then the material in the rest of the course will most likely also be successfully mastered.
It is not unusual to hear a student describe their past experience with a mathematics course with something like the following: "I had an algebra class 10 years ago, I hated it, I got a 'D' in it, I put this course off until the last possible semester in my college career...". With many students, statistics is initially greeted with mixed feelings of fear and anger. Fear because of the reputation of mathematics courses, anger because the course is required for a major or minor and the student has had no choice in its selection. It is my feeling that these emotions inhibit the learning of the material. It is my experience that before any real learning may take place the student must relax, have some success with the material, and accept the course. It is the responsibility of the instructor to deal with these negative emotions. If this is not done, the course might just as well be taught by a combination of books and computers.
Another difficulty is sometimes encountered by the instructor of a statistics course is the student who has done very well in almost all other courses, and has a desire to do very well in a statistics course. In some cases it is the first time that the material does not come easily to the student, with the student not understanding everything the instructor says. Panic sets in, tears flow, or perhaps the student is simply never seen in a statistics classroom again.
The student must be willing to accept the fact that a complete understanding of statistics may not be obtained in a single introductory course. Additional study, perhaps graduate work, is necessary to more fully grasp the area of statistics. This does not mean, however, the student has achieved nothing of value in the course. Statistics may be understood at many different levels; it is the purpose of this course to introduce the material in a manner such that the student achieves the first level.
Emphasis has been placed in several different directions during the past two decades with respect to the teaching of statistics in the behavioral sciences. The first, during the 1950's and perhaps early 1960's saw a focus on computation. During this time, large electro-mechanical calculators were available in many statistics laboratories. These calculators usually had ten rows and ten columns of number keys, and an addition, subtraction, multiplication, and division key. If one was willing to pay enough money, one could get two accumulators on the top; one for sums and one for sum of squares. They weighed between 50 and 100 pounds, filled a desktop, made a lot of noise, and cost over $1000. Needless to say, not very many students carried one around in their backpack.
Because the focus was on computation, much effort was made by the writers of introductory textbooks on statistics to reduce the effort needed to perform statistical computations using these behemoths. This was the time period during which computational formulas were developed. These are formulas that simplify computation, but give little insight into the meaning of the statistic. This is in contrast to definitional formulas, that better describe the meaning of the statistic, but are often a nightmare when doing large-scale computation. To make a long story short, students during this phase of the teaching of introductory statistics ended up knowing how to do the computations, but had little insight into what they were doing, why they did it, or when to use it.
The next phase was a reaction to the first. Rather than computation, the emphasis was on meaning. This was also the time period of the "new math" in grade and high schools, when a strong mathematical treatment of the material was attempted. Unfortunately, many of the students in the behavioral sciences were unprepared for such an approach and ended up knowing neither the theory nor the computational procedure.
Calculators available during this time were electronic, with some statistical functions available. They were still very expensive, over $1000, and would generally not fit in a briefcase. In most cases, the statistics texts still retained the old computational formulas.
The current trend is to attempt to make statistics as simple for the student as possible. An attitude of "I can make it easier, or more humorous, or flashier than anyone else has in the past" seems to exist among many introductory statistics textbooks. In some cases this has resulted in the student sitting down for dinner and being served a hot fudge sundae. The goal is admirable, and in some cases achieved, but the fact remains that the material, and the logic underlying it, is difficult for most students.
My philosophy is that the statistical calculator and statistical computer packages have eliminated the need for computational formulas; thus they have been eliminated from this text. Definitional formulas have been retained and the student is asked to compute the statistic once or twice "by hand." Following that, all computation is done using the statistical features on the calculator.
This is analogous to the square root function on a calculator. How many times do people ever use the complex algorithm they learned in high school to find a square root? Seldom or never. It is the argument of the present author that the square root procedure should be eliminated from the mathematics classroom. It gives little or no insight into what a square root is or how it should be used. Since it takes only a few minutes to teach a student how to find a square root on a calculator, it is much better to spend the remaining classroom time discussing the meaning and the usefulness of the square root.
In addition, an attempt has been made to tie together the various aspects of statistics into a theoretical whole by closely examining the scientific method and its relationship to statistics. In particular, this is achieved by introducing the concept of models early in the course, and by demonstrating throughout the course how the various topics are all aspects of the same approach to knowing about the world.
Grade assignment will be made on a point system based on total points at the end of the semester. Assignment will be made by taking 90%, 80%, 70%, and 60% of total points, based on the highest score in the class for A, B, C, D, and F, respectively. Some adjustment may be made at the discretion of the instructor. The different components of the course will be weighted with the following values:
In the past semesters a total of from 310 to 315 points have been necessary to earn an "A" in the course, 270 to 275 to earn a "B", etc. The total number of points varies slightly from semester to semester because different numbers of multiple-choice questions have been included on the tests.
SOME ADVISE - Classroom attendance is strongly encouraged. Roll will be taken during the first part of the class until the instructor learns the names of the students. Attendance does not directly affect your grade, although on the basis of past experience, it is the truly exceptional student who can afford to miss more than two or three classes. Getting behind is almost always fatal in terms of completion of the course and grading.
The correct way to study the material is to read the text before coming to class, listen carefully in class, following along with the problems, take notes in the margins and space provided in this text, reread carefully the text at home, follow the examples, and finally, do the assigned homework.
Throughout the book various icons or pictures will be placed in the left margin. They should be loosely interpreted as follows:
Important Definitional Formula - MEMORIZE
A Computational Procedure.
An Example of a Procedure
I wrote this book for a number of reasons, the most important one being my students. As I taught over a period of years, my approach to teaching introductory statistics began to deviate more and more from traditional textbooks. All too often students would come up to me and say that they seemed to understand the material in class, thought they took good notes, but when they got home the notes didn't seem to make much sense. Because the textbook I was using didn't seem to help much, I wrote this book. I took my lectures, added some documentation, and stirred everything with a word processor with this book as the result.
This book is dedicated to all the students I have had over the years. Some made me think about the material in ways that I had not previously done, questioning the very basis of what this course was all about. Others were a different challenge in terms of how I could explain what I knew and understood in a manner in which they could comprehend. All have had an impact in one way or another.
Three students had a more direct input into the book and deserve special mention. Eve Shellenberger, an ex-English teacher, earned many quarters discovering various errors in earlier editions of the text. Craig Shealy took his editorial pencil to a very early draft and improved the quality greatly. Wendy Hoyt has corrected many errors in the Web Edition. To all I am especially grateful.
I wish to thank my former dean, Dr. Jim Layton, and my department head, Dr. Fred Maxwell, both of whom found the necessary funds for hardware and software acquisition to enable this project. Recently I have received funds from the Southwest Missouri State University academic vice president, Dr. Bruno Schmidt, to assist me in the transfer of this text from paper to Web format.