Understanding Political Science Statistics

Observations and Expectations in Political Analysis

Peter Galderisi

• Publisher: Routledge
• Year: 2015
• eBook ISBN: 9781136819490
• Topic: Politics & International Relations
• Subtopic: Politics
• Index: Politics & International Relations

In politics, you begin by asking theoretically interesting questions. Sometimes statistics can help answer those questions. When it comes to applied statistics, students shouldn't just learn a vast array of formula—they need to learn the basic concepts of statistics as solutions to particular problems. Peter Galderisi demonstrates that statistics are a summary of how to answer the problem: learn the math but only after learning the concepts and methodological considerations that give it context.

With this as a starting point, Understanding Political Science Statistics asks students to consider how to address a research problem conceptually before being led to the appropriate formula. Throughout, Galderisi looks at problems through a lens of "observations and expectations," which can be applied to myriad statistical techniques, both descriptive and inferential. This approach links the answers researchers get from their individual data analysis to the research designs and questions from which these analyses are derived.

By emphasizing the underlying logic of statistical analysis for greater understanding and drawing on applications and examples from political science (including law), the book illustrates how students can apply statistical concepts and techniques in their own research, in future coursework, and simply as an informed consumer of numbers in public discourse.

The following features help students master the material:

• Legal and Methodological sidebars highlight key concepts and provide applied examples on law, politics, and methodology;

• End-of-chapter exercises allow students to test their mastery of the basic concepts and techniques along the way;
• A Sample Solutions Guide provides worked-out answers for odd-numbered exercises, with all answers available in the Instructor's Manual;
• Key Terms are helpfully called out in both Marginal Definitions and a Glossary;
• A Companion Website (www.routledge.com/cw/galderisi) with further resources for both students and instructors;
• A diverse array of data sets include subsets of the ANES and Eurobarometer surveys; CCES; US Congressional district data; and a cross-national dataset with political, economic, and demographic variables; and
• Companion guides to SPSS and Stata walk students through the procedures for analysis and provide exercises that go hand-in-hand with online data sets.

CHAPTER 1

Political Science, the Scientific Method, and Statistical Analysis

An Overview

CONTENTS

• The Language of Science
• The Structure of Hypotheses
• The Beauty of Hypotheses for Research
• The Logic of Causation—A Review
• Key Terms
• Questions and Exercises

Learning Objectives:

• To understand that political science can be studied scientifically
• To understand the language of science
• To understand what a hypothesis is and how it should be structured
• To understand the components necessary to make a causal argument

Political Science is the study of actors and agencies within a legal, institutional setting. As with any science, the observations derived from measuring and analyzing actual data must follow from the creation of questions of interest that are derived from a proper and logically reasoned generalized statement of the relationship between or among types of political events. In order to understand, for example, the reasons why Barack Obama did better in most areas in 2008 than John Kerry did in 2004, we need to investigate the reasons why individuals choose to vote the way that they do in more than just those two elections. Comparing differences between those two years may help to confirm or disconfirm our general explanation of why candidates win and by what margin. But so can comparing any other two elections. And they should also, by finding irregularities or anomalies, help us to understand the circumstances under which our statistical findings do not match our causal expectations.

Statistics can help us to summarize our findings for any given two years, or any other combination of events, but, as mentioned in the Preface, they can do so only as tests that are naturally derived and implied from theoretically sound methodological formulations. Without proper and generalizable measurements and designs, they are of interest, they are suggestive, but they are not fully scientifically consequential. They are an important but not the only essential component of scientific inquiry.¹

Part of the nature of scientific inquiry is the sharing of knowledge. One’s study is not to be read in a vacuum, but in the context of other work investigating similar, and sometimes quite different, political, economic, social, and psychological relationships. Knowledge cannot be shared if we are all speaking our own language. Part of the difficulty of sharing in the “social,” sometimes pejoratively categorized as the “soft” sciences, is that, unlike many of the more traditional or “harder” sciences, we often use terms for which there is no or little common definitional agreement. What do we mean by “democracy,” “political authority,” and, even more narrowly, “voter intention” (as the 2000 recounts in Florida and 2008 in Minnesota demonstrated)? Does the discipline share the same common understanding of these terms as say, “wind velocity,” “distance,” or “white cell count”? As science is partly defined as this “sharing of common knowledge,” a lack of a common vocabulary hampers the growth of our discipline.

This text, with its greater, if not exclusive, interest in statistical analysis will not try to single-handedly resolve all of these definitional conflicts (other than to advise one to state as clearly and precisely as possible what one means). It will, however, offer a brief accounting of the definition of basic terms that are the core of scientific inquiry.²

The Language of Science

Following is a simple vocabulary for terms of scientific research that will be used throughout this text. Later, we will discuss how these terms interact with each other.

Units of Analysis, Case, or Fact

The units of analysis, case, or fact are the entities, drawn from a known or theoretical population, from which we take or may later be able to take measurements. Some examples follow:

units of analysis, case, or fact Entities from which measurements are taken.

1. Peter Galderisi
2. My dog, Treana
3. The chair I’m now sitting on as I write this text
4. The United States
5. The European Union
6. Congressman Darrell Issa (my current representative)

For example, in an exit survey of voters, each surveyed individual would be a “unit of analysis.” The “units” of analysis would be survey respondents. In a comparative study of election laws in different countries, the unit of analysis would be each country. The number of cases for each study is usually abbreviated as n or N. For example, if we were to list ballot forms in the different states, N would equal 50 (51 if Washington, D.C., is included for analysis). If we were to study roll call votes in the U.S. Congress, N would equal 435 for the House and 100 for the Senate. The number of cases in an exit poll would equal the actual number surveyed.

Properties, Concepts, and Variables

Properties exist in nature whether we know them or not, concepts are our guesses about those properties, and variables are our observable or potentially observable measurements of those concepts. The important factor about properties is that, unlike units of analysis, they are generalizations or abstractions—characteristics, behaviors, attitudes—that can be used to discuss and describe many different units of analysis. Any unit of analysis can be described using categories of a host of properties. For example, in describing Peter Galderisi, we can use gender (category male), ethnicity (category Italian-American), marital status (happily married), height (69 inches in stocking feet), age (62 years, probably 63 when this is finally published), weight (don’t ask), hair color (brown with a dusting of gray), partisan preference, ideology, vote choice, views about gay rights, and so forth. Notice that these properties can not only be used to “define” me, but also other units of analysis. Those units don’t even have to share the same biological type. All of the unit of analysis examples listed previously can be described by their age. “Partisan preference” can be used to describe both myself and Congressman Issa (although my dog does seem to react differently given which political pundit is on TV).

number of cases The total units of analysis from which measurements are taken.

properties/concepts The generalizations we believe are important to measure from our cases.

variable The actual, real-world measurement of properties/concepts.

What is both important and difficult is to ascertain which properties are most important in our analyses of political behavior. Gender and ethnicity (or at least the values associated with them) are probably important determinants of partisan preference. Height is probably not (although it may act as a surrogate for gender or ethnic differences). Although we tend to eliminate certain properties as politically irrelevant in a given analysis, we may find out later that they are very relevant (keep this in mind when we discuss the importance of randomization later on).

Students often confuse variables (which must vary) with the categories of those variables (which don’t). “How one voted for president” would be a common variable in an exit poll. The “Republican percentage of the presidential vote” would be a variable measured from each state (or voting precinct). Each possible response or measurement is referred to as a category of the relevant variable. For each voter, the category would correspond to the vote choice (Republican, Democratic, Green, etc.). For each state, a category would be listed as the percentage (46%, 54%, etc.) that voted Republican in each state.

Laws and Hypotheses

Laws exist in nature, and hypotheses are our guesses about laws.³ These are our generalized guesses or expectations about how properties relate to each other. Stating that “men are more likely to support Republican candidates than are women” is a statement about our expectations about the interaction between gender and partisan preference. Hypotheses (more on this later) are never just about two facts (we don’t just compare one man and one woman—although that might act as a limited test of that hypothesis)—they are generalizations about the relationship between and among properties that can be tested in many ways. Stating that “I am more likely to vote Republican than my wife” is an expected outcome that naturally follows from our hypothesis. It is a “factual statement,” that is, one that can be proved true or false on limited investigation, not a hypothesis itself (it’s not a generalization). We’ll discuss “how to create a good” hypothesis in the next section.

laws/hypotheses The actual and perceived relationships between or among properties/concepts.

factual statement Test of a hypothesis that is proved true or false on limited investigation.

Table 1.1 Listing and Comparison of Terms

In Nature	Our Guesses about Them	Our Measurements of Them
Property	Concept	Variable
Law	Hypothesis	Test Implication/Factual Statement

In this text, I will take the liberty to use “properties” and “concepts” interchangeably. “Variable” will be used when we discuss their actual measurement in the real world.

Theories

Theories are a broader generalized knowledge that help to explain why properties are related to the way we hypothesize. Let’s take a simple example. Do any of us have to see someone cut a limb from a tree to be able to predict that it will fall to the ground? Well, no, for two reasons:

theories/theory sketches A broad explanation of why we expect to observe what our hypotheses predict.

1. Experience—you have seen this occur so often that you are fairly certain about its predictive force (common sense). A myriad of observations have always met your expectations.
2. Theoretical link—it can not only be predicted but also explained by the theory of gravity, stated simply as:

• Objects of mass greater than zero are attracted to each other.
• The attraction favors the object of greater mass.
• A limb has less mass than the earth.
• Therefore: if I cut a tree limb, it will “fall” to the ground unless held up by some other means.

Notice the importance of theory here. It not only predicts that but explains why the tree limb should fall. Like a hypothesis, it has generalizable utility. It can predict and explain the falling of any severed tree limb, the unfortunate collapse of a building whose structure is compromised, and the falling of a duck when shot (thereby removing its innate ability to keep itself airborne). However, the theory of gravity helps explain so much more. It helps to explain why the moon revolves around the earth as we revolve around the sun. It helps to explain tidal patterns. Many scientists believe that gravitational pulls might help to explain the timing of certain types of earthquakes. To really move out there, some believe that planetary gravitational forces can help to explain mood swings. Remember that the term “lunatic” is derived from the Latin name for the moon....

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Contents
• Tables, Figures, and Sidebars
• Preface
• 1 Political Science, the Scientific Method, and Statistical Analysis: An Overview
• 2 How Do We Measure and Observe?
• 3 Central Tendency as Summary Observation
• 4 Dispersion/Variation/Goodness of Fit as Summary Observation
• 5 Standardized Scores and Normal Distributions: The Concept of Relative Observation
• 6 An Intuitive Introduction to Inference and Hypothesis Testing
• 7 Hypothesis Testing and the Concept of Association: Observations and Expectations about the Difference between Means
• 8 Inferential Statistics for Proportions
• 9 Measuring Association for Nominal and Ordinal Data
• 10 Research Design and the Use of Control Variables
• 11 Different by How Much? Linear Regression
• 12 Retracing Our Methodological Steps: Hypotheses, Multiple Regression, and the Effects of Third Variables
• Concluding Remarks
• Glossary
• Sample Solutions Guide
• Index