techniques in public and nonprofi t management. Th e last chapter in this section explains how to read and interpret regression output generated by statistical soft- ware packages, which is often complicated and diffi cult to understand. Th e chapter, thus, provides a needed skill that is too often overlooked.
Th e fi nal part of the book discusses “Special Topics in Quantitative Man- agement”: performance measurement and decision theory. A full treatment of linear programming can be found on the companion Website for the book. Th ese materials expose students to techniques for measuring organizational perfor- mance, diff erent models of logical analysis, bases for decisions, and evaluation of alternatives. In sum, this book provides essential coverage pertaining to the NASPAA Standards for Accreditation in public aff airs in administration and the NACC Curricular Guidelines for Nonprofi t Administration.
arranged in a table or chart and for data that have not, which we aff ectionately term “raw data.” Once you have calculated or read the average for a group or distribution of data, the next question to ask is how closely the data cluster or spread about this average—that is, whether the observed values or observations are relatively concentrated or dispersed about the measure of central tendency.
Chapter 6, “Measures of Dispersion,” introduces the two major statistics for mea- suring dispersion in a sample of data: the variance and its close relative, the stan- dard deviation. It also discusses the range and other statistics.
Th e next part of the book addresses probability. Probability can be confusing for students to understand; do not become discouraged! To learn the basic rules and applications of probability, please see Chapter 7, which presents an introduc- tion to the topic. In that chapter, you will learn the basic law of probability as well as what is meant by a priori probabilities, posterior probabilities, joint prob- abilities, and conditional probabilities. With this background, the remaining chap- ters on probability will be much easier to follow.
Chapter 8 presents the most common probability distribution, the normal curve. Th e familiar bell-shaped curve has numerous uses and applications in pub- lic and nonprofi t administration. When data follow a normal distribution, it is practical and easy (OK, maybe not easy, but surely within your reach) to deter- mine the percentage of job applicants who fall above or below a criterion score on a test of job-related skills. Or you can fi nd the score that distinguishes the top 5% of applicants for further consideration (for example, those applicants for whom a follow-up interview is warranted).
Have you ever wanted to know the probability that an agency could hire 3 minorities for 10 positions when 50% of the job applicants were minorities?
For problems similar to this one, Chapter 9 introduces the binomial probability distribution. Th e chapter also shows how the normal distribution can be applied to simplify complex binomial problems, provided certain conditions are met. Th e chapter following discusses other useful probability distributions for public and nonprofi t managers. Th e hypergeometric probability distribution is used when the manager wants to make a generalization from a sample to a fi nite population.
Th e Poisson and the exponential probability distributions are used whenever the manager needs to include time or distance in a probability statement—for example, 1.2 computer failures per day or 15 potholes per 100 meters.
Part IV explores statistical inference and focuses on the issue of how the man- ager can generalize (infer) results from a small sample of data to the much larger population from which the sample was drawn. Th is technique is useful in its own right and also to support advanced statistical procedures presented later in the book, such as regression analysis. Because the public or nonprofi t manager must work almost always with a sample rather than the full population of data—but seeks reliable information about the entire population—knowledge of statistical inference is essential. To learn how to estimate the value of the mean or average for a population from a sample of data, consult Chapter 11. Th is chapter also discusses procedures for constructing confi dence bands or intervals around the mean estimate.
Chapter 12 applies the techniques of statistical inference to testing hypoth- eses. Although it is not possible to avoid the risk of error in inferring from a sample of data to the population (we cannot be sure of results if we do not have population information), public or nonprofi t managers may be willing to take an acceptable risk in drawing an inference. Th e chapter shows how, by using the techniques of classical hypothesis testing on a small sample of data, the manager can make a decision regarding the full population—for example, that the average number of times the population of agency clients seeks assistance is four times or more per year, or that the average is less—at the risk of error of, say, 5%. You will thus learn a technique that in the long run will allow you to make the correct decision 95% of the time but be in error the remaining 5% (remember, because we do not know the “answers” in the population, we cannot be right all the time).
Chapter 13 shows how to estimate population proportions, rather than mean or average values, from a sample—for example, the proportion (or percentage) of motorists in a county who drive faster than 65 miles per hour on a stretch of highway. For those situations in which the manager needs to compare the per- formance or characteristics of two groups (for example, experimental and control groups, groups before and after the implementation of a program or interven- tion or treatment, and so forth), Chapter 14 explains how to test for diff erences between groups using the statistical technique called analysis of variance.
Beginning with Part V, the remainder of the book deals with relationships between two or more variables. Th e study of relationships between two variables is called bivariate analysis. Bivariate statistical techniques can help to answer myriad research and practical questions: Is agency budget related to performance? Do police patrols reduce crime? Does greater inclusiveness in government hiring lead to a more responsive bureaucracy? Does government contracting with nonprofi t organizations produce more effi cient delivery of services? Do employees in non- profi t organizations display greater job motivation than those in other sectors of the economy? Do smaller nonprofi t organizations adapt more quickly to their environ- ments than larger ones? Is there a relationship between delegating decision-making authority to lower levels of the organization and innovativeness of employees?
Part V explains how to construct tables and analyze data at the nominal and ordinal levels of measurement—that is, information measured in terms of catego- ries (for example, gender) or rating scales (for example, attitude toward balancing the federal budget, or clients’ evaluations of the training provided by a volunteer center). Chapter 15 shows how to use percentages to analyze and interpret tables called contingency tables or cross-tabulations that pair data from two nominal or ordinal variables. Chapter 16 builds on this foundation to provide more sophis- ticated techniques for analyzing tables, including statistical inference (chi-square) and measures of association (gamma, lambda, and so forth). Chapter 17 dis- cusses statistical control table analysis, a procedure for examining the relationship between two variables while taking into account or “controlling for” or “holding constant” a third variable. Th e analysis of three or more variables simultaneously presented in this chapter introduces multivariate analysis, a topic covered more extensively in later chapters of the text.
Part VI is concerned with relationships between variables assessed on equal interval scales, or “interval” data, such as variables measured in years, dollars, or miles. Chapter 18 begins the discussion with an “Introduction to Regression Analysis,” a highly fl exible and often used statistical technique that is helpful in a variety of managerial situations in the public and nonprofi t sectors. Th e chapter shows how a line or linear relationship depicted in a graph or set of coordinate axes can summarize the relationship between two interval variables—for instance, the relationship between the number of intake workers at a government facility and the number of clients who receive service in a given day. Chapter 19 explains the assumptions and limitations of regression analysis. Estimating and predicting trends in the future based on past data is the subject of Chapter 20 on time series analysis. Consult this chapter to forecast such trends as future population, the number of people likely to volunteer to government agencies, service usage, sew- age output, the number of organizations that will participate in the community walk-a-thon to raise cancer awareness, and other over-time information impor- tant to public and nonprofi t managers.
Chapter 21, “Multiple Regression,” extends this technique to the multivari- ate context: It shows how to use regression to analyze and understand relation- ships among three or more variables. For example, how well can the average age of housing and the percentage of renter-occupied buildings in a neighborhood explain or predict the incidence of fi res across a city? To what extent do the num- ber of volunteers working in nonprofi t agencies and the number of community events sponsored by these organizations aff ect the amount of money collected in their annual fund-raising campaigns?
Chapter 22, on interrupted time series analysis, explains how to estimate the impact of a program or policy over time. Th e manager can use this technique to evaluate whether a program, such as a senior citizens’ center or a municipal vol- unteer offi ce, has had a short-term, long-term, or short-term temporary impact (or perhaps no impact) on the health and welfare of city residents.
Chapter 23 focuses on the interpretation of regression output—that is, out- put generated by statistical software packages. Th e earlier chapters in this sec- tion (Chapters 18–22) present a variety of regression examples in equation form to illustrate how relationships between variables can be summarized using linear equations. Statistical software packages generally do not present regression results in equation form, however, which can make the leap from textbook to computer applications and printout confusing. Although it is perfectly acceptable to write up regression results in either equation or summary table form (the format used by most statistical software packages), managers need to have a clear understand- ing of the similarities and diff erences between these formats to interpret and use the information provided eff ectively. Regression analysis is almost always per- formed with computers. As a result, public and nonprofi t managers need expo- sure to how regression is carried out and presented in statistical software packages before conducting such analyses on their own.
Part VII presents two special topics in quantitative management that are sometimes useful to public and nonprofi t managers. From years of teaching, as
well as feedback from instructors who have been kind enough to adopt this book (thank you!) and their students (thank you, too!), we know that not all students will be exposed to this part of the book. But some students are—and we include treatment of these topics as an aid and courtesy to them. Many of you will need to use these techniques later in your career in public or nonprofi t management.
Statistical methods are often used as tools for measuring and improv- ing o rganizational performance in both government and nonprofit settings.
Chapter 24 on performance measurement techniques provides an overview of some of the key issues that managers in both sectors need to know when d esigning performance measurement systems and reporting performance results to external audiences. If you are interested in how to make decisions given various amounts of information, Chapter 25 on decision theory can be very helpful. Th e chapter presents useful ways to evaluate alternatives and select among them.
Previous editions of the book included a chapter on linear programming.
Th is technique is useful for decision situations that involve maximizing or mini- mizing some output under certain constraints. Th at chapter has been moved to the companion Website for the book.
Following the chapters in the book, you will fi nd other materials useful for the study of applied statistics for public and nonprofi t administration. For those motivated to learn more about statistics (don’t laugh—by the time you have read a chapter or two, this student could be you!), we have included an Annotated Bibliography with a brief description of each entry. Th e bibliography contains a wide assortment of texts valuable for assistance and reference. For ease of use of the book, you will also fi nd, at the back, a Glossary of key terms that have been boldfaced at their fi rst appearance in the text except in the fi rst chapter, where they are highlighted in italics to draw attention to later use. And, of course, to make the book self-contained, you will fi nd all of the statistical tables (normal, t-test, etc.) essential for applied statistics for public and nonprofi t administra- tion both for relevant courses and for present and future careers. Finally, you will quickly make friends with the section containing answers to the odd-numbered computational questions from the problem sets at the end of each chapter.
Whenever possible, we have attempted to include problems faced by public and nonprofi t administrators in the real world. Many of our midcareer as well as more senior students suggested problems and examples for the book. Although all the data and problems are hypothetical, they represent the types of situations that often confront practicing public and nonprofi t administrators. We hope that you fi nd them useful and interesting.
Now you have a road map for the book. Good luck on the journey!
2
U
sing a statistical approach in public and nonprofi t administration begins with measurement. Measurement is the assignment of numbers to some phenomenon that we are interested in analyzing. For example, the eff ectiveness of army offi cers is measured by having senior offi cers rate junior offi cers on various traits. Educational attainment may be measured by how well a student scores on standardized achievement tests. Good performance by a city bus driver might be measured by the driver’s accident record and by his or her record of running on time. Th e success of a nonprofi t agency’s fund-raising drive might be measured by the amount of money raised. How well a nonprofi t agency’s board of directors represents client interests might be measured by the percentage of former or current clients on the board.Frequently, the phenomenon of interest cannot be measured so precisely, but only in terms of categories. For example, public and nonprofi t administra- tors are often interested in characteristics and attitudes of the general popu- lace and of various constituency groups. We can measure such things as the racial and gender composition of the individuals in these groups; their state of residence or their religious preferences; their attitudes toward a particular agency or government in general; their views on space exploration, public spending, or the tax treatment of nonprofi t organizations; and so on. Although such variables do not have quantitative measurement scales, it is still possible to measure them in terms of categories—for instance, white versus nonwhite;
female versus male; favor tax decrease, favor no change, favor tax increase; and so on. Although these phenomena cannot be measured directly with numerical scales, they are important variables nonetheless. Public and nonprofi t admin- istrators need to know how to measure, describe, and analyze such variables statistically.
In many managerial situations the manager does not consciously think about measurement. Rather, the manager obtains some data and subjects them to anal- ysis. Th ere are problems with this approach. In Chapter 12 we will discuss an example in which the Prudeville police crack down on prostitution in the city.
Under the leadership of the police chief, daily arrests by the vice squad increase from 3.4 to 4.0. Based on these numbers, the police chief claims a successful pro- gram. Th is example illustrates a common measurement problem. Th e city council
Measurement
of Prudeville was concerned about the high level of prostitution activity, not the low level of prostitution arrests. Conceivably the number of prostitution arrests could be positively related to the level of prostitution activity (i.e., more prosti- tution arrests indicates greater prostitution activity). In this situation, the police chief ’s data may reveal increased prostitution, not decreased prostitution. In fact, the only thing an analyst can say, given the police chief ’s data, is that the number of prostitution arrests increased.
In this chapter, we will discuss some of the important aspects of measure- ment, both in theory and in application.