Success at Statistics

A Worktext with Humor

Fred Pyrczak

• Publisher: Routledge
• Year: 2016
• ISBN:
  9781351968058
• Edition: 6
• Topic: Psychology
• Subtopic: Research & Methodology in Psychology
• Index: Psychology

• This comprehensive text covers all the traditional topics in a first-semester course.

• Divided into 67 short sections, this book makes the topics easy to digest. Students regularly get positive reinforcement as they check their mastery with exercises at the end of each section.

• Each exercise is based on a humorous riddle. If the answer to a riddle makes sense, students know all their answers for that exercise are correct. If not, they know they need to check their answers.

• Short sections make it easy to customize your course by assigning only those sections needed to fulfill your objectives.

• A comprehensive basic math review at the end of this book may be used to help students whose math skills are rusty.

• Thoroughly field-tested for student interest and comprehension. The short sections and humor-based, self-checking riddles are greatly appreciated by students.

• Contains Part D on effect size, which provides technical solutions to issues raised in Part C (such as the limitations of inferential statistics).

New to this edition:

Section 1: Explains the importance of statistical techniques in the advancement of scientific knowledge.

Section 11:

Provides practice with the summation operation before using it in multiple statistical tests.

Section 27:

This section on z -scores explains how to translate a percentile rank into a raw score.

Section 30:

Underlines the importance of figural representations of data, explains how to identify the most appropriate figure, and discusses how to label figures effectively.

Section 41:

Provides a deeper understanding of the relationship between p -values and critical values in a statistical test.

Appendix J:

A summary table of all statistical equations and guidelines for choosing a particular statistical test.

Table 1:

The format and discussion for the Table of the Normal Curve has been changed to a more conventional presentation of this statistical tool.

Section 23 Introduction to Sampling

Inferential statistics help researchers to make inferences (i.e., generalizations) from samples to populations. For instance, we might be interested in the attitudes of all registered nurses in Maryland toward individuals with AIDS. The nurses would constitute the population. If we administered an AIDS attitude scale to all these nurses, we would be studying the population, and the summarized results (such as means and standard deviations) would be referred to as parameters. If we studied only a sample of the nurses, the summarized results would be referred to as statistics.

No matter how researchers sample, it is always possible that the statistics obtained do not accurately reflect the population parameters that would have been obtained if researchers had studied the entire population. In fact, researchers always expect some amount of error when they have sampled.

If sampling creates errors, why do researchers sample? First, it is not always possible, for economic and physical reasons, to examine an entire population. Second, with proper sampling, researchers can obtain highly reliable results and can estimate the amount of error to allow for in the interpretations of the data.

The most important characteristic of a good sample is that it be free from bias. A bias exists whenever some members of a population have a greater chance of being selected for inclusion in the sample than others. Following are some examples that would produce biased samples:

• A professor wants to study the attitudes of all sophomores at a college (the population) but asks only those enrolled in her introductory psychology class (the sample) to participate in the study. Note that only those who are in the class have a chance of being selected. All other sophomores have no chance.
• A politician wants to predict the results of a citywide election (the population) but queries the intentions of only voters whom he encounters in a large shopping mall (the sample). Note that only those in the mall whom he decides to approach have a chance of being selected. All other voters have no chance.
• A magazine editor wants to determine the opinions of all rifle owners in the United States (the population) on gun-control measure but mails questionnaires only to those who subscribe to her magazine (the sample). Note that only subscribers have a chance to respond and that all other rifle owners have no chance.

In the previous examples, samples of convenience (also called accidental samples) were used, which increased the odds that some would be selected and reduced the odds that others would—but there is an additional problem. Even those who have a chance of being included may refuse to participate. This problem is often referred to as volunteerism. Volunteerism is presumed to create a bias because those who decide not to participate have no chance of being included in the data. Furthermore, many studies comparing participants with nonparticipants suggest that participants tend to be more highly educated and from higher socioeconomic-status (SES) groups than their counterparts. Efforts to reduce the effects of volunteerism include offering rewards, stressing to potential participants the importance of the study, and making it easy for people to respond, such as by providing them with a self-addressed, stamped envelope.

To eliminate bias, some form of random sampling is needed. A classic form of random sampling is simple random sampling.¹ In this technique, each member of the population is given an equal chance to be selected. A simple way to accomplish this with a small population is to put the name of each member of a population on a slip of paper, thoroughly mix the slips, and have a blindfolded assistant select the number desired for the sample. After the names have been selected, efforts must be made to encourage all of those selected to participate. If some members refuse, as often happens, we have a biased sample even though we started by creating an equal chance that any one person's name would be selected.

Suppose that we are fortunate. We have selected names using simple random sampling, and we have obtained the cooperation of everyone selected. In this case, we have an unbiased sample. Can we be certain that th...