Understanding Political Science Statistics: Observations and Expectations in Political Analysis

364 Pages·2015·2.88 MB·English

by  Peter Galderisi

Understanding Political
Science Statistics
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 demon-
strates 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 sta-
tistical 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 under-
standing and drawing on applications and examples from political science (includ-
ing 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 con-
cepts 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.
Peter Galderisi has taught political science methods and statistics for more than
three decades, and is currently a lecturer and local internship director in the
Political Science Department at the University of California, San Diego. Previ-
ously, Galderisi was a Professor or Visiting Professor at Utah State, UCLA, UC
Santa Cruz, and Cal State Fullerton. He specializes in U.S. political parties,
campaigns and elections, American political development, interest groups, and
election law.
This page intentionally left blank
Understanding Political
Science Statistics
Observations and Expectations
in Political Analysis
Peter Galderisi
First published 2015
by Routledge
711 Third Avenue, New York, NY 10017
and by Routledge
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2015 Taylor & Francis
The right of Peter Galderisi to be identified as author of this work has been asserted by him in
accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form
or by any electronic, mechanical, or other means, now known or hereafter invented, including
photocopying and recording, or in any information storage or retrieval system, without permission
in writing from the publishers.
Trademark notice: Product or corporate names may be trademarks or registered trademarks, and
are used only for identification and explanation without intent to infringe.
Library of Congress Cataloging-in-Publication Data
Galderisi, Peter.
Understanding political science statistics : observations and expectations in
political analysis / Peter Galderisi.
pages cm
1. Political statistics. 2. Political science—Statistical methods.
3. Political science—Methodology. I. Galderisi, Peter F. II. Title.
JA71.7.G35 2015
320.01'5195—dc23
2014030207
ISBN: 9780415890052 (pbk)
ISBN: 9780203830031 (ebk)
Typeset in Adobe Garamond Pro
by Apex CoVantage, LLC
This volume is dedicated to my friend and colleague of over three decades,
William L. Furlong. About eight years ago, as I was leaving another academic
institution, Bill took my wife, Holly, aside and said that “Peter needs to finish
this text. It will be good for his soul.” Its completion, I believe, has been good
for both of our souls.
v
This page intentionally left blank
Contents
Tables, Figures, and Sidebars xiii
Preface xix
1 Political Science, the Scientific Method, and
Statistical Analysis: An Overview 1
The Language of Science 2
Units of Analysis, Case, or Fact 2
Properties, Concepts, and Variables 3
Laws and Hypotheses 4
Theories 5
The Structure of Hypotheses 7
Falsifiability 7
Not Immediately Verifiable 9
The Beauty of Hypotheses for Research 10
Increasing the Number and Types of Tests 10
Broadening Our Frame of Reference or Context 11
Uncovering Theoretical Relevance 11
The Logic of Causation—A Review 12
Test 12
Theory or Theory Sketch 12
Triangulization 14
Alternate Explanations 14
“Potential” Measurement Problems 15
“Potential” Design Problems 15
Key Terms 17
Questions and Exercises 17
vii
CONTENTS
2 How Do We Measure and Observe? 20
Statistical Measurement—An Introduction 21
Reliability of Measurement 23
Internal Validity of Measurement 24
Reliability versus Internal Invalidity 25
Precision in Measurement 26
Levels of Measurement—Mathematical Assumptions 27
Nominal Data 27
Ordinal Data 28
Interval Data 29
Levels of Measurement—Conceptual Assumptions 30
Frequency Distributions as Measurement and Observation 32
Absolute Frequency 33
Relative Frequencies: Percentages and Proportions 34
The Importance of Standardization 35
Cumulative Frequency 37
From Nominal to Interval Data 38
Graphs as Visualizations of Our Observations 39
Bar Chart 39
Pie Chart 40
Frequency Polygon and Line Charts 40
Time Series Charts 42
One More Example 46
Measuring Properties and the Importance of Categorization 46
Key Terms 48
Questions and Exercises 48
3 Central Tendency as Summary Observation 54
Measures of Central Tendency 55
Mode 55
Understanding Statistics as Games of Chance 57
Median 58
Mean 60
Formulas as Shorthand Devices 65
Formula for the Mean Derived from a Frequency Distribution 67
A Note on Medians and Means 69
Appendix: 2012 Presidential Vote 69
Key Terms 71
Questions and Exercises 71
4 Dispersion/Variation/Goodness of Fit as Summary
Observation 77
Measures of Diversity for Nominal Data 78
Variation Ratio 79
Index of Qualitative Variation 81
viii
CONTENTS
Measures of Diversity for Ordinal and Interval Data 89
The Range and Interquartile Range 90
Deviation Scores 91
Mean Absolute Deviation 93
Variance (Mean Squared Deviation) 94
Standard Deviation 95
A Summary Example with Aggregated Data 97
Key Terms 98
Questions and Exercises 99
5 Standardized Scores and Normal Distributions:
The Concept of Relative Observation 102
How Well Off Are We? 103
Standardization and Z-Scores 106
A Policy Example 109
Furthering Our Understanding of Z-Scores 110
Relative Placement: Why a Student Should Never Ask
That Grades Be Curved 113
A Cautionary Tale 119
Key Terms 119
Questions and Exercises 120
6 An Intuitive Introduction to Inference and
Hypothesis Testing 122
Inferential Statistics 123
The Law of Large Numbers 125
The Sampling Distribution of Means and the Central Limit Theorem 127
An Example: The Gender Gap in Wages 132
Hypothesis Testing 136
Considerations in Sampling 137
t-Tests and Statistical Hypothesis Testing 140
Statistical Hypothesis Testing and One-Tailed Tests 142
Key Terms 143
Questions and Exercises 143
7 Hypothesis Testing and the Concept of Association:
Observations and Expectations about the Difference
between Means 146
Comparison of Two Means 148
The Marriage Gap and Feelings toward Parties 154
Special Comment on Significance Tests 157
Appendix: Comparison of Two Variables, Same or
Matched Groups 158
Key Terms 159
Questions and Exercises 159
ix