1.2 Overview of Topics

What are we going to be studying in this book? Figure 1.1 summarizes the major topics and their organization.

Allow me to unpack the figure just a bit. The greatest portion of the book is devoted to procedures in which a single measure is analyzed at a time: one variable or “univariate.” What is the height of the average adult male in the United States? Or what is the weight of the average adult male? The last two chapters of the book introduce procedures for analyzing measures that are taken in pairs: two variables or “bivariate.” What is the relationship between height and weight for adult males in the United States? Yes, you are correct that there are statistical procedures for analyzing relations among more than two measures—“multivariate” statistics—but those procedures are for more advanced courses in statistics.

Coverage of both univariate and bivariate statistics begins with the study of “descriptive statistics.” Descriptive statistics are a toolkit of analyses for presenting and summarizing a collected set of observations. They include procedures for tabling and graphing data as well as statistical calculations that summarize important properties of the dataset (e.g., mean, standard deviation). Descriptive statistics are always the first step in the analysis of any dataset because they are our way of creating a coherent picture of the dataset.

In some situations, characterizing the results for a dataset is all that needs to be done. For example, a chief executive officer (CEO) who wants information about the employees of the company has all the needed information once data are gathered on all the employees. In statistical language, we would say that the set of all employees is the entire “population” of interest. However, in most situations in science, our dataset does not consist of all the observations in the population we are trying to learn about; rather, our dataset is a subset or “sample” of observations from the population. We still use descriptive statistics to characterize the sample, but we then conduct additional analyses to try to determine whether we can trust our description of the sample as a description of the population. This process of trying to generalize from a sample to a population involves the use of “inferential statistics.” As you might guess, this logical leap from sample to population involves a lot of logical machinery, so this is where most of our attention will be focused. That does not mean that inferential statistics are more important than descriptive statistics; it just means that they are more complex.

Chapter 2 “Variables and Their Distributions” and Chapter 3 “Measures of Properties of Distributions” cover descriptive procedures in univariate statistics. Our introduction to inferential statistics will begin in Chapter 4 “Introduction to Probability” by considering the general characteristics of research studies. This will give us a context for understanding the role of statistics in research and it will establish the central role of probability in the process of drawing general conclusions about populations based on the sample of observations collected in a study. Most of Chapter 4 will be dedicated to the study of basic probability concepts and laws.

As we will learn, different inferential procedures are used for distinct types of outcome measures. In our study of univariate statistics, we will introduce the normal distribution in Chapter 5 “The Normal Distribution: Theoretical Foundations” and use it to introduce the major inferential procedures in Chapter 6 “Inferential Procedures Based on the Normal Distribution” and Chapter 7 “The Power of a Hypothesis Test”.

Chapter 8 “Student’s t for Inferences about a Single Mean” and Chapter 9 “Student’s t for Inferences about the Difference between Two Means” will continue our development of procedures for analyzing means and differences between means. We will then introduce procedures for analyzing variances in Chapter 10 “One-Factor Analysis of Variance” and Chapter 11 “Two-Factor Analysis of Variance”. Our coverage of univariate statistics will conclude the study of procedures for analyzing frequency data in Chapter 12 “Using the Chi-Square Distribution to Analyze Frequencies”.

The final two chapters of the book will explore bivariate statistics. After learning methods of describing bivariate data in Chapter 13 “Describing Bivariate Distributions”, we will develop procedures in Chapter 14 “Inferences about Correlation and Regression” for testing whether our descriptions of a dataset may be generalized to the population from which we sampled the observations in our dataset. Those procedures will allow us to determine whether two variables are related in a population (i.e., correlation), and if so, what the best description of the relationship is (i.e., regression).

If my brief description of the topics does not mean much to you at this point, not to worry. The point is that there is a lot to learn! Although I cannot learn the material for you, I can guide you through the material and help you gradually construct an understanding of the concepts and procedures of statistics. Let’s begin.