Explaining Psychological Statistics

Barry H. Cohen

• Publisher: Wiley
• Year: 2013
• ISBN:
  9781118652145
• Edition: 4
• Topic: Psychology
• Subtopic: Research & Methodology in Psychology
• Index: Psychology

A clear and accessible statistics text— now fully updated and revised

Now with a new chapter showing students how to apply the right test in the right way to yield the most accurate and true result, Explaining Psychological Statistics, Fourth Edition offers students an engaging introduction to the field. Presenting the material in a logically flowing, non-intimidating way, this comprehensive text covers both introductory and advanced topics in statistics, from the basic concepts (and limitations) of null hypothesis testing to mixed-design ANOVA and multiple regression.

The Fourth Edition covers:

• Basic statistical procedures
• Frequency tables, graphs, and distributions
• Measures of central tendency and variability
• One- and two-sample hypothesis tests
• Hypothesis testing
• Interval estimation and the t distribution

Part One

Descriptive Statistics

Chapter 1

Introduction to Psychological Statistics

A. CONCEPTUAL FOUNDATION

If you have not already read the Preface, please do so now. Many readers have developed the habit of skipping the Preface because it is often used by the author as a soapbox, or as an opportunity to give his or her autobiography and to thank many people the reader has never heard of. The Preface of this text is different and plays a particularly important role. You may have noticed that this book uses a unique form of organization (each chapter is broken into A, B, and C sections). The Preface explains the rationale for this unique format and explains how you can derive the most benefit from it.

What Is (Are) Statistics?

An obvious way to begin a text about statistics is to pose the rhetorical question, “What is statistics?” However, it is also proper to pose the question “What are statistics?”—because the term statistics can be used in at least two different ways. In one sense statistics refers to a collection of numerical facts, such as a set of performance measures for a baseball team (e.g., batting averages of the players) or the results of the latest U.S. census (e.g., the average size of households in each state of the United States). So the answer is that statistics are observations organized into numerical form.

In a second sense, statistics refers to a branch of mathematics that is concerned with methods for understanding and summarizing collections of numbers. So the answer to “What is statistics?” is that it is a set of methods for dealing with numerical facts. Psychologists, like other scientists, refer to numerical facts as data. The word data is a plural noun and always takes a plural verb, as in “the data were analyzed.” (The singular form, datum, is rarely used.) Actually, there is a third meaning for the term statistics, which distinguishes a statistic from a parameter. To explain this distinction, I have to contrast samples with populations, which I will do at the end of this section.

As a part of mathematics, statistics has a theoretical side that can get very abstract. This text, however, deals only with applied statistics. It describes methods for data analysis that have been worked out by statisticians, but does not show how these methods were derived from more fundamental mathematical principles. For that part of the story, you would need to read a text on theoretical or mathematical statistics (e.g., Hogg & Craig, 1995).

The title of this text uses the phrase “psychological statistics.” This could mean a collection of numerical facts about psychology (e.g., how large a percentage of the population claims to be happy), but as you have probably guessed, it actually refers to those statistical methods that are commonly applied to the analysis of psychological data. Indeed, just about every kind of statistical method has been used at one time or another to analyze some set of psychological data. The methods presented in this text are the ones usually taught in an intermediate (advanced undergraduate or graduate level) statistics course for psychology students, and they have been chosen because they are not only commonly used but are also simple to explain. Unfortunately, some methods that are now used frequently in psychological research (e.g., structural equation modeling) are too complex to be covered adequately at this level.

One part of applied statistics is concerned only with summarizing the set of data that a researcher has collected; this is called descriptive statistics. If all sixth graders in the United States take the same standardized exam, and you want a system for describing each student's standing with respect to the others, you need descriptive statistics. However, most psychological research involves relatively small groups of people from which inferences are drawn about the larger population; this branch of statistics is called inferential statistics. If you have a random sample of 100 patients who have been taking a new antidepressant drug, and you want to make a general statement about the drug's possible effectiveness in the entire population, you need inferential statistics. This text begins with a presentation of several procedures that are commonly used to create descriptive statistics. Although such methods can be used just to describe data, it is quite common to use these descriptive statistics as the basis for inferential procedures. The bulk of the text is devoted to some of the most common procedures of inferential statistics.

Statistics and Research

The reason a course in statistics is nearly universally required for psychology students is that statistical methods play a critical role in most types of psychological research. However, not all forms of research rely on statistics. For instance, it was once believed that only humans make and use tools. Then chimpanzees were observed stripping leaves from branches before inserting the branches into holes in logs to “fish” for termites to eat (van Lawick-Goodall, 1971). Certainly such an observation has to be replicated by different scientists in different settings before becoming widely accepted as evidence of toolmaking among chimpanzees, but statistical analysis is not necessary.

On the other hand, suppose you want to know whether a glass of warm milk at bedtime will help insomniacs get to sleep faster. In this case, the results are not likely to be obvious. You don't expect the warm milk to knock out any of the subjects, or even to help every one of them. The effect of the milk is likely to be small and noticeable only after averaging the time it takes a number of participants to fall asleep (the sleep latency) and comparing that to the average for a (control) group that does not get the milk. Descriptive statistics is required to demonstrate that there is a difference between the two groups, and inferential statistics is needed to show that if the experiment were repeated, it would be likely that the difference would be in the same direction. (If warm milk really has no effect on sleep latency, the next experiment would be just as likely to show that warm milk slightly increases sleep latency as to show that it slightly decreases it.)

Variables and Constants

A key concept in the above example is that the time it takes to fall asleep varies from one insomniac to another and also varies after a person drinks warm milk. Because sleep latency varies, it is called a variable. If sleep latency were the same for everyone, it would be a constant, and you really wouldn't need stati...