Integrative Statistics for the Social and Behavioral Sciences

Renee R. Ha, James C. Ha

• Publisher: SAGE Publications, Inc
• Year: 2011
• ISBN:
  9781452237299
• Edition: 1
• Topic: Mathématiques
• Subtopic: Probabilités et statistiques

Designed to engage students and lower their "fear factor", Integrative Statistics for the Social and Behavioral Sciences is a concise, user-friendly text that prepares students to use statistics in the real world. Providing depth and breadth of statistical tests, the text focuses on choosing the appropriate statistical analysis, and shows how to interpret the output and present the results.

PART I

DESCRIPTIVE STATISTICS

1. Introduction to Statistics: What Are You Getting Into?

2. Getting Started With Statistics

3. Frequency Distributions and Graphing

4. The Mean and Standard Deviation

5. The Normal Distribution, Standardized Scores, and Probability

CHAPTER 1

Introduction to Statistics

What Are You Getting Into?

What Is Statistics?

What Is Our Approach to Statistics?

Practical Details Before We Can Move On

Summary

WHAT IS STATISTICS?

This book addresses the topic of statistics, but what exactly do we mean by statistics? Statistics is a branch of applied mathematics that involves the collection and interpretation of data and the use of mathematical principles to draw conclusions about the results of our observations. Stated another way, statistics is a field of mathematical study that addresses how data that are collected in a study (such as the number of accidents at a particular intersection) can reveal patterns and how to evaluate those patterns based on the likelihood of that pattern occurring by chance. Patterns that are considered to be unlikely occurrences if chance alone is operating are then said to be occurring for reasons other than chance (such as poor visibility in the intersection or some other variable that we believe might be affecting the outcome of our study).

WHAT IS OUR APPROACH TO STATISTICS?

This book is intended for those of us who use statistics as a tool to understand the data that they collect in their research or to understand the data collected by others in their research. Thus, we will not delve too deeply into the theoretical basis behind the mathematics that we teach, but you will definitely be using some of your skills in mathematics in this course, and it would be a good idea for you to review some basic college mathematics textbooks if you feel you have difficulty recalling things like the proper order that you follow when you have multiple operations in a single problem (e.g., always do what is in the parentheses first). There will be statistical tests that you will learn to conduct by hand. However, while we feel that requiring some calculations to be done by hand is important in teaching the underlying basis of statistical interpretation, this can be done for a limited number of tests and still accomplish the conceptual goals of the course.

In addition, we will emphasize how the steps you take in calculating and evaluating a statistical test by hand compare to interpreting a printout of the same statistical test in two different computer software packages. Because the statistical terminology varies among textbooks and software packages, it is critical that you are trained to understand the conceptual basis to the labels. That will be easier for you if you have been exposed to more than one style of output. Truthfully, very few scientists calculate statistical tests by hand, and when they do, it is only for the simple tests. Thus, we will provide examples in the appropriate chapters that demonstrate the step-by-step calculations done by hand and then show the output from the same data in Microsoft’s Excel and SPSS Inc.’s Statistical Package for the Social Sciences (SPSS). We chose these software packages because they are much different from one another but commonly used, and SPSS has a student version. We will highlight the numbers that match the numbers that we calculated by hand, and we will define all of the output since there are more numbers provided by computer software packages than you normally use when you hand calculate the same tests. The additional numbers have proven confusing to students when they get to their laboratory course if they have only been trained in the hand calculation techniques.

Beginning in Part II, you will be introduced to a flowchart that will guide you on how to choose the appropriate statistical test for a given data set and experimental design, and that flowchart will be built up chapter by chapter as you learn more tests. In fact, we feel that choosing the appropriate test is the most important concept in undergraduate statistics because the computer can do the analysis for you only if you know which statistical test is appropriate. Students commonly come to their laboratory courses without the ability to choose the appropriate test because they have learned statistics one chapter at a time and there was only one statistical test per chapter.

We will also introduce you to the concept of a “general linear model.” This is often neglected in an undergraduate course, but it is an important and useful concept. On the basis of our coverage of this model, you will be able to analyze data using the general linear model on a statistics software package (such as SPSS) if you ever need to do so. You will be able to apply this more modern technique to appropriate data sets and will also better understand the mathematical relationships between tests that are commonly performed in the behavioral sciences (independent t test, paired t test, analysis of variance [ANOVA], linear regression), all of which you will hear about in later chapters.

PRACTICAL DETAILS BEFORE WE CAN MOVE ON

Before we move on into new material in Chapter 2, there are a couple of practical details to cover, including a discussion of rounding and features of a statistical calculator. The details of this material might be altered by your instructor for the specific details of your class, but this information should prove useful for most students.

A Short Discussion of Rounding

The rules about rounding vary a bit based on the field of study. We will follow the rule that is common in the social sciences, which is to round to two decimal places. For example, if you have a number such as 164.0665, we would round that number using rules that are based on the number in the third decimal position.

Rounding Rules

If the number in the third decimal position is > 5, we would round the second decimal position up by one unit. If the number in the third decimal position is < 5, we would retain the number in the second decimal. If the number was exactly 5, then we would look at the next decimal place (fourth) but apply the same “less than or greater than 5” rule.

Example

For the number 164.0665, the number in the third decimal position is a 6, and thus we would round the number in the second decimal position (also a 6) up one unit (7). Thus, our newly rounded number would be reported as 164.07.

However, the number 1...

Table of contents

• Cover Page
• Dedication Page
• Title Page
• Copyright
• Brief Contents
• Detailed Contents
• About the Authors
• Preface
• Acknowledgments
• Part I. Descriptive Statistics
• Part II. Introduction to Hypothesis Testing
• Part III. Additional Hypothesis Tests
• Homework Answers
• Appendix: Statistical Tables
• Glossary
• References
• Index