When the effect of one independent variable on the dependent variable is conditional upon values of another dependent variable, we have an interactive relationship.If the effect of one variable on the dependent variable changes across various values of a second independent variable, we have an interactive relationship.This chapter provides examples of interactive relationships and how to model them using an interaction term in a linear regression.Attention is given to how to interpret interaction terms in linear regression and statistical significance for both interactions with interval level variables and dummy variables.Marginal effects graphs are illustrated to further explain interactive relationships.

Dispersion describes the spread of the data or how it varies from its mean.The chapter begins with the calculation of the variance and then the more important standard deviation, along with their interpretation.Students learn how to calculate these measures by hand and in the R Commander.Other measures of dispersion like skewness and kurtosis are described.The range and interquartile range are also calculated using the R Commander software for ordinal variables.

The chapter compares and contrasts various statistics software including R, STATA, SPSS, and the R Commander.Detailed instructions on how to download R, R Studio, and the R Commander package are provided so that students can use the R Commander for the remainder of the book.Uploading data into the R Commander and basic data recoding are discussed.

The chapter begins with an applied example describing the limitations of bivariate regression and the need to include multiple independent variables in a regression model to explain the dependent variable.The logic of multivariate regression is discussed as it compares to bivariate regression.Running a multivariate regression in the R Commander and interpretation of the results are the main foci of the chapter, with particular attention to the beta coefficients, y-intercept, and adjusted R-squared.Generating the multivariate regression equation from the R Commander output is covered, along with engaging in prediction using this equation.Finally, interpretation of dummy independent variables in a multivariate regression is covered.

The chapter covers the use of ordinal dependent variables like Likert scale measures for research hypotheses.The Wilcoxon Rank Sum test is described using a public administration example.Students learn how to conduct the rank sum test by hand and with the R Commander.Interpretation and statistical significance are the foci of the R Commander output.The Wilcoxon Signed Rank test is explained as is how it differs from the Rank Sum Test.Instructions for conducting and interpreting the Signed Rank test in the R Commander are included.

Students are instructed on how to create the most common graphs in public administration research and data visualization.Correct data setup for each graph is illustrated through the use of datasets in the Companion Site.Graphs include bar graphs, histograms, line graphs, boxplots, and scatterplots.Steps to produce these graphs in R Commander are covered using public administration examples and datasets.

Chapter 2 covers the basics of research design.It is written so that students without any research design experience or coursework can learn common research designs to enable them to conduct statistical analyses in the text.Hypotheses development with variable construction (dependent and independent variables) are covered and applied to experimental and non-experimental designs.Survey methods including question construction and implementation of surveys is presented.