We are now ready to introduce magnetic fields, which are generated by electrical currents and which apply forces on moving charges and current-carrying wires. Historically, magnetic effects in lodestones, an iron ore that can be magnetized, have been known for a long time. The first magnetic compasses date back to about 1000 BCE, and the ancient Chinese are believed to have used such devices for navigation as early as 1100 CE. The properties of magnetic fields can be derived from a number of observations of magnetic effects that have been recorded over many years. One of the earliest such observations, by Hans Christian Oersted in 1820, was that a current-carrying wire exerts a torque on a permanent magnet (such as a compass). Current-carrying wires can also exert forces on each other, as first observed by Biot and Savart and more fully characterized by Ampère. Finally, beams of charged particles, such as electrons in a cathode ray tube (see TechNote 3.4), are deflected when in the presence of current-carrying wires. Each of these phenomena can be described quantitatively in terms of a magnetic field produced by current distributions, as we will discuss throughout this chapter.

With the introduction in the previous chapter of the electric field and electric potential, and their properties in materials, we are now ready to examine the energy stored in electric fields, the electric forces that can be exerted on objects, and the capacitance between conductors. We cover these topics in this chapter. We also introduce additional methods that can be used for determining electric fields and potentials.

As we have been discussing electric and magnetic effects throughout this text, we have been developing a set of equations, known collectively as Maxwell’s Equations, that describe the properties of these fields in a very general sense. These equations are named after James Clerk Maxwell, whose contributions are discussed in Biographical Note 7.1. The development of Maxwell’s Equations has been critical to our understanding and application of electromagnetic effects, as they govern such diverse effects as are present in capacitors, transformers, and electric generators, which we have already examined, and free-wave propagation, transmission lines, waveguides, and antennas, which we have not yet discussed. Before we can undertake our study of these new topics, we must first complete the development of Maxwell’s Equations, which are not quite finished. As we will show shortly, there is an inconsistency in these equations as they stand to this point, an inconsistency that can be rectified by introducing a new term, known as the displacement current, to Ampère’s Law. This additional term is the final piece of the puzzle, and with its inclusion Maxwell’s Equations can be used to describe wave propagation, allowing us to understand (at an overview level, at least) the principles that govern our wireless routers, microwave ovens, and cable and satellite TV systems. In this chapter, we will introduce the displacement current, redefine the potential functions for time-varying fields, and re-examine the boundary conditions that must be satisfied at the interface between two different materials.

Analysis of Variance (ANOVA) is a commonly used test in public administration research when the dependent variable is measured at the interval level and the independent variable is measured at the nominal level with more than two categories.The chapter covers when and how to use ANOVA along with the assumptions of the ANOVA test.Conducting ANOVA in the R Commander and interpreting the output and statistical significance of the test are the main foci of the chapter.

Students are introduced the logic, foundation, and basics of statistical inference. The need for samples is first discussed and then how samples can be used to make inferences about the larger population. The normal distribution is then discussed, along with Z-scores to illustrate basic probability and the logic of statistical significance.

The focus of the chapter is on turning concepts into measurable variables, also known as operationalization.Best practices in created variable based on the concept are covered.The differences between nominal, ordinal, and interval level variables are discussed along with their relevance for statistical tests later covered in the book.The importance of measurement validity and reliability and their implications for research provide another focus of the chapter.

This chapter focuses on the most common statistical tests used when the dependent variable is measured at the interval level and the independent variable is nominal with two categories.The one-sample t-test is first introduced so that students can understand comparing a value of the dependent variable to another value.Then, the independent samples t-test is discussed, followed by the dependent samples t-test when the unit of analysis is compared over time, especially in a pre-post setting.All of these tests are also illustrated with R Commander instruction and interpretation of the t-statistic and statistical significance.

Using linear regression requires assumptions that must be met.The criteria for using regression is discussed including the need for the dependent variable to be interval and to have a linear relationship with the independent variable(s).Omitting relevant variables and problems are discussed, along with explaining the importance of the error term in a regression.Detecting multicollinearity in the R Commander is illustrated, along with implications of and solutions for multicollinearity.The effects of heteroscedasticity are discussed with an illustration of it.

This chapter is devoted to extensive instruction regarding bivariate regression, also known as ordinary least squares regression (OLS).Students are presented with a scatterplot of data with a best-fitting line drawn through it.They are instructed on how to calculate the equation of this line (least squares line) by hand and with the R Commander.Interpretation of the statistical output of the y-intercept, beta coefficient, and R-squared value are discussed.Statistical significance of the beta coefficient and its implications for the relationship between an independent and dependent variable are described.Finally, the use of the regression equation for prediction is illustrated.

The final chapter of the textbook covers logistic regression, a statistical test used when the dependent variable is dichotomous or binary.OLS regression should not be used when the dependent variable is binary.The first discussion focuses on the limitations of OLS in this situation.The logit equation is presented and then steps for conducting a logistic regression in the R Commander are explained.Interpretation of the logistic regression output using odds ratios, percent change in odds, and predicted probabilities is discussed.Applied examples are used to better illustrate when to use logistic regression.

The chi-square test is used when both the dependent and independent variables are measured at the nominal level.The first step to running a chi-square test is to construct a contingency table.Students are instructed on how to do so by hand and with the R Commander.Assumptions of the chi-square test follow.Running the chi-square test in the R Commander is then discussed along with interpretation and statistical significance.The chapter concludes with limitations of the chi-square test.

Central tendency describes the typical value of a variable.Measures of central tendency by level of measurement are covered including the mean, median, and mode.Appropriate use of each measure by level of measurement is the central theme of the chapter.The chapter shows how to find these measures of central tendency by hand and in the R Commander with detailed instructions and steps.Skewed distributions and outliers of data are also covered, as is the relationship between the mean and median in these cases.

Best practices in data acquisition and entry are the central theme of this chapter.Correct entry of variables and data in spreadsheets like Excel is discussed along with common problems of data entry that may prevent software from reading and analyzing data correctly. Typical practices of entering data for nominal, ordinal, and interval variables give the student information on how to enter data in Excel for these variables.The purpose of codebooks and composing them to match data are discussed.Different types of data including cross-sectional, time-series, and panel are presented to the student.Finally, common sources of public administration data are listed and described.

The introductory chapter introduces students to contemporary issues in public administration research like Covid-19, environmental problems, social equity, public service motivation, and general challenges in public service.These contemporary issues and challenges have been identified by the National Academy of Public Administration.The chapter discusses how data can be manipulated to tell a particular side of a story. Therefore, data and research ethics are also covered. Students are introduced to ethics in human subjects research and associated best practices.