Abstract
Introduction
The classic statistical inference techniques are mostly based on distributional assumptions, but it is not uncommon for those assumptions to be violated in a real-world problem. When observations are ranked or ordered values, it is not appropriate to assume that samples come from any specific family of distribution. Even when the outcomes are measurements on an interval scale, the distribution of the sample might be skewed, peaked, flatted, or include outliers. In both cases, we can use nonparametric or distribution-free inferences, which postulate less strict assumptions than do parametric inferences. Since their validity relies on milder underlying conditions, nonparametric procedures tend to be more robust to the distributional feature, with a slight loss of power than are parametric procedures (Gibbons & Chakraborti, 2011; Hettmansperger & McKean, 2010). For this reason, nonparametric statistical methods have been widely used in social science, education, sociology, psychology, or economics, where quantitative methods are often applied.
Contents
Many books on nonparametric statistics exist: Some focus on applications of nonparametric techniques and others attempt to explain the theory behind the techniques. Nonparametric Statistics for Applied Research, written by Linebach, Tesch, and Kovacsiss, focuses on applications of nonparametric methods in real-world problems, but its approach is quite different from typical statistical books.
The book consists of fictional dialogues of consultants who work for a political campaign of the Governor of California. The multidisciplinary team, including a medical doctor, a policy analyst, a clinical psychologist, and a crime analyst, solve various problems about sex offender laws. A data set about sex offenders in California is introduced in Chapter 2 and analyzed throughout the book using various nonparametric statistical procedures.
This book covers widespread nonparametric statistical techniques, beginning with tests for distributional shape and tests of randomness of data in Chapter 3. Tests of association for nominal variables (Chapter 4), two ordered variables (Chapter 5), and more than two ordered variables (Chapter 6 and 7) are introduced. Transitioning to tests of difference in Chapter 8, nonparametric methods for testing difference between samples in interval scale (Chapter 9) and in ordered scale (Chapter 10), difference in probability (Chapter 11), and difference in more than three groups (Chapter 12) are described. The results are summarized in the final report for the Governor in Chapter 13. All of these statistical methods are explained from the point of view of researchers who are not sufficiently familiar with statistical methods. In addition, rather than theoretical statisticians, the authors are applied psychologists in Forensic Studies and Public Policy.
Strengths and Weaknesses
The unique feature of the book is that it brings together positive and negative aspects that standard textbooks on nonparametric statistics do not have. Since all discussions start from real-world problems and then statistical methods are provided to answer them, readers understand why they need to learn the technical method and how statistics can be applied to real life. Since most of the imaginary consultants in this book are not well acquainted with traditional statistics, it explains statistical jargon such as dichotomous, dependent variable, power, and matched sample in straightforward language. Statistical concepts that are confused often in practice, such as p values and Type I and Type II errors, are also described well using a real example. The book also illustrates the calculation of statistics in a detailed manner. Furthermore, it is valuable to observe conflicts among researchers on a multidisciplinary team during a decision-making process.
On the other hand, readers might have difficulty finding the techniques they need, because the book is not organized according to the type of statistical methods, but instead to the questions that arise in a real situation. The authors have definitely made an effort to categorize the research questions into two types of statistical problems, namely, tests of association and tests of difference, and to introduce the statistical procedures according to each. The decision trees in Chapter 1 provide an outstanding guide to find an appropriate nonparametric technique. However, it seems insufficient to search for core ingredients among the narrative dialogues and the list of contents without revealing the statistical methods contained in each chapter.
This book describes statistical decision-making procedures logically in a practical way, but a few basic but important statistical concepts are presented ambiguously and need to be clarified. First, a nonparametric statistical method is not assumption-free, and random sampling is assumed for both parametric and nonparametric methods for hypothesis testing (Gibbons & Chakraborti, 2011; Sprent & Smeeton, 2007). A data set is called a random sample if observations are independently drawn from the same distribution that is not necessarily in a specific parametric family. Therefore, the fact that the sample in the book consists of sex offenders that are not chosen randomly from the population but collected from the sex offenders residing near the headquarters of the campaign cannot justify the use of nonparametric procedures over parametric alternatives. In addition, many nonparametric tests assume the shape of the population. It would be worth mentioning that, for example, Wilcoxon’s signed rank test assumes that the distribution of the random variables is symmetrical (Wilcoxon, Katti, & Wilcox, 1970) and that the Kruskal–Wallis test assumes the k-number of populations have approximately the same distributional form (Kruskal & Wallis, 1952).
Second, “mutually exclusiveness” does not imply that two samples are “independent.” In order to test for differences between two populations, the book proposes the Kolmogorov–Smirnov two-sample test and the Mann–Whitney U test for independent samples, and the sign test and Wilcoxon’s rank sum test for matched samples. We call two samples independent if subjects in both samples are randomly selected and so are not related. Two samples are called mutually exclusive if they do not share any common elements. In practice, it is occasionally observed that mutually exclusive sets are regarded as independent sets. However, although there is no overlap between two samples, they might not be independent. For example with twin studies, when a pair of twins are divided between two groups, observations in the two groups are paired in a systematic way, but they do not share any individuals.
Final Remarks
The audience for this book could be applied researchers and theoretical statisticians, but the benefits of the book would lie in different perspectives. Readers who are specialized in social science and are less familiar with nonparametric statistics will learn about the decision-making procedure using nonparametric statistical methods without being distracted by equations and proofs. However, I recommend using this book as supplementary material accompanied by a traditional nonparametric statistics book because it will help to organize various nonparametric techniques in a more systematic way. Readers who have a more theoretical background in statistics will learn how applied problems drive statistical analyses, how applied research in a multidisciplinary team works, and how statistical ideas can be shared with coworkers efficiently.