# POLSC251: Research Methods in Political Science

Unit 6: Quantitative Methods: Inferential Statistics   In the last unit, you learned about descriptive statistics, where the goal is to describe and compare variables within a given sample. In this unit, you will learn to use inferential statistics, where the goal is to use a sample to make inferences about the characteristics or relationships in a larger population. You will first learn how to create a sample that represents the qualities and characteristics of a larger population. From there, the unit will delve into the application of inferential statistics, discussing ways of determining whether the sample that you have created is truly representative of the larger population in question. You will learn about statistical significance and other indicators that help determine the strength of your sample and hypothesis and look further into the relationships between variables.

The unit will then discuss the concept of correlation as well as the more complex relationships that regression analysis enables you to discover. Regression analysis allows you to understand the condition and strength of an association between an independent variable and a dependent variable. In this section, you will first learn about more basic, linear regression and then move on to more complex, multivariate, multiple regression analysis. By the end of the unit, you should be able to define a representative sample and run both simple correlation and complex regression analyses to uncover statistically significant relationships between variables in a model.

This unit should take you approximately 20.5 hours to complete.

☐    Subunit 6.1: 2 hours

☐    Subunit 6.2: 6.5 hours

☐    Subunit 6.2.1: 30 minutes

☐    Subunit 6.2.2: 2 hours

☐    Subunit 6.2.3: 2 hours

☐    Subunit 6.2.4: 2 hours

☐    Subunit 6.3: 6 hours

☐    Subunit 6.4: 3 hours

☐    Subunit 6.5: 3 hours

Unit6 Learning Outcomes
Upon successful completion of this unit, you should be able to - describe the basic theory that drives inferential statistics; - discuss the calculations for some inferential statistics; and - interpret some of the statistics that would result from standard and typical methods used in political science.

6.1 Understanding Inferential Statistics   - Reading: Understanding Inferential Statistics The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

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6.1.1 Making Comparisons   Note: Making comparisons between two or more social constructs or variables is at the heart of research design and analysis. Cross-tabulations and chi-square analyses discussed below is a good introduction to making such comparisons. This subunit is covered by the material beenath subunit 6.1.

6.1.2 Cross-Tabulations   - Reading: University of Indiana: Robert S. Michael’s “Cross-tabulation & Chi Square” Link: University of Indiana: Robert S. Michael’s “Cross-tabulation & Chi Square” (PDF)

`````` Instructions: Please read this article (8 pages). This article
describes in detail how cross-tabulations are executed and how chi
square tests are used to test for statistical significance.

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• Reading: Social Science Research and Instructional Council: California State University’s “Chapter 5: Cross Tabulations” Link: Social Science Research and Instructional Council: California State University’s “Chapter 5: Cross Tabulations” (HTML)

Instructions: Read this chapter on cross-tabs. The chapter’s focus on how to conduct and interpret correlational analyses is important in thinking about how you might conduct cross-tabs.

6.1.3 Research Using the Chi-Square Statistic   - Reading: Wellesley College: “The Χ2 (AKA chi-square) Distribution” Link: Wellesley College: “The Χ2 (AKA chi-square) Distribution” (PDF)

Instructions: Read this presentation on Chi Square analyses. Pay close attention to the instructive examples.

Reading this presentation should take approximately 30 minutes.

6.1.4 Calculating Variance and Standard Deviation   - Web Media: YouTube: hknuth123’s “Calculating Variance and Standard Deviation” Link: YouTube: hknuth123’s “Calculating Variance and Standard Deviation” (YouTube)

`````` Instructions: Watch this video. This video is essential to your
understanding of all the statistics in the rest of this unit; if
necessary, please view the video multiple times to reinforce your
understanding.

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`````` Instructions: Watch this video. This video will help you understand
the meaning of standard deviation in practical terms. If necessary,
please view the video multiple times to reinforce your
understanding.

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6.2 Statistical Significance Testing & Hypothesis Testing   6.2.1 Defining Statistical Significance   - Reading: George Mason University, Statistical Assessment Service: “What Does It Mean for a Result to Be Statistically Significant?” Link: George Mason University, Statistical Assessment Service: “What Does It Mean for a Result to Be Statistically Significant?” (HTML)

`````` Instructions: Please read this article, which provides a basis for
understanding statistical significance. This is crucial to
understanding the rest of statistical concepts in this unit.

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`````` Instructions: Please read this tutorial. You must click next at the
upper right hand corner of the text to move through each of the 21
short entries. There will be a question at the end of some of these
short entries. You may attempt to answer each question, and then

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• Assessment: Wadsworth Cengage Learning’s Statistic Workshops: “Chi-Square Quiz” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Chi-Square Quiz” (HTML)

Instructions: Click on the link above to access Wadsworth Cengage Learning’s webpage. Then, please click on Workshop Quiz from the menu on the left of the webpage, and complete the quiz.

`````` Instructions: Please read this tutorial. You must click next at the
upper right hand corner of the text to move through each of the 17
short entries. There will be a question at the end of some of these
short entries. You may attempt to answer each question, and then
error.

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• Assessment: Wadsworth Cengage Learning’s Statistic Workshops: “Standard Error Quiz” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Standard Error Quiz” (HTML)

6.2.4 Assessing the Evidence for Hypotheses: P-values and Significance Tests   - Reading: Wadsworth Cengage Learning’s Statistic Workshops: “Hypothesis Testing” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Hypothesis Testing” (HTML)

`````` Instructions: Please read this tutorial. You must click next at the
upper right hand corner of the text to move through each of the 16
short entries. There will be a question at the end of some of these
short entries. You may attempt to answer each question, and then
testing.

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• Assessment: Wadsworth Cengage Learning’s Statistic Workshops: “Hypothesis Testing Quiz” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Hypothesis Testing Quiz” (HTML)

6.3 Difference of Means Tests   - Reading: Wadsworth Cengage Learning’s Statistic Workshops: “Tests of Means” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Tests of Means” (HTML)

`````` Instructions: Please read this tutorial. You must click next at the
upper right hand corner of the text to move through each of the 34
short entries. There will be a question at the end of some of these
short entries. You may attempt to answer each question, and then
differences in means. This reading is applicable to Subunits 6.3.1
through 6.3.4.

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• Assessment: Wadsworth Cengage Learning’s Statistic Workshops: “Tests of Means” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Tests of Means” (HTML)

6.3.1 One Sample Z-Test   Note: This topic is covered in the material beneath subunit 6.3. This is one type of difference of means tests that relies on z-scores described in Subunit 6.2.2.

6.3.2 One Sample t-Test   - Reading: Wadsworth Cengage Learning’s Statistic Workshops: “Single Sample t-Test” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Single Sample t-Test” (HTML)

`````` Instructions: Please read this article. You must click next at the
upper right hand corner of the text to move through each of the 3
short entries. There will be a question at the end of some of these
short entries. You may attempt to answer each question, and then
t-test.

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• Assessment: Wadsworth Cengage Learning’s Statistic Workshops: “Single Sample t-Test” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Single Sample t-Test” (HTML)

6.3.3 T-test for Dependent Means   Note: This topic is covered by the material beneath subunit 6.3. This is one type of difference of means tests that is used when we want to know whether there is a difference between means that are linked or dependent on each other.

6.3.4 T-test for Independent Means   - Reading: Wadsworth Cengage Learning’s Statistic Workshops: “Independent versus Repeated t-Tests” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Independent versus Repeated t-Tests” (HTML)

`````` Instructions: Please read this tutorial. You must click next at the
upper right hand corner of the text to move through each of the 12
short entries. There will be a question at the end of some of these
short entries. You may attempt to answer each question, and then
t-test.

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• Assessment: Wadsworth Cengage Learning’s Statistic Workshops: “Independent versus Repeated t-Tests Quiz” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Independent versus Repeated t-Tests Quiz” (HTML)

6.4 Correlation   6.4.1 Defining Correlation   - Reading: William M.K. Trochim’s Research Methods Knowledge Base: “Correlation” Link: William M.K. Trochim’s Research Methods Knowledge Base: “Correlation” (HTML)

`````` Instructions: Please read this article that describes the basic
principles of how to determine if variables are correlated with one
another.

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`````` Instructions: Please read this tutorial. You must click next at the
upper right hand corner of the text to move through each of the 20
short entries. There will be a question at the end of some of these
short entries. You may attempt to answer each question, and then
article covers how correlation coefficients are calculated and
used.

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• Assessment: Wadsworth Cengage Learning’s Statistic Workshops: “Correlation Quiz” Link: Wadsworth Cengage Learning’s Statistic Workshops: “Correlation Quiz” (HTML)

6.5 Multivariate Analysis   - Reading: William M.K. Trochim’s Research Methods Knowledge Base: “General Linear Model” Link: William M.K. Trochim’s Research Methods Knowledge Base: “General Linear Model” (HTML)

`````` Instructions: Please read this article. Also, click on each of the
hyperlinks in the assigned article and read those as well. You can
then click your back button to get back to the original article. You
do not need to click on the hyperlinks in the articles that were
linked to the original article. Just click back to the original
article. This reading describes the basic principles of the linear
model. Pay particular attention to the latter half of the article,
which talks about the use of the model with multiple variables.

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• Reading: AUCO Czech Economic Review: Madeleine O. Hosli and Marc C. J. Uriot’s “Dimensions of Political Contestation: Voting in the Council of the European Union before the 2004 Enlargement” Link: AUCO Czech Economic Review: Madeleine O. Hosli and Marc C. J. Uriot’s “Dimensions of Political Contestation: Voting in the Council of the European Union before the 2004 Enlargement” (PDF)

Terms of Use: The material above has been reposted with permission by Madeleine O. Hosli and Marc C. J. Uriot. It can be viewed in its original form here.

6.6 Regression and Multivariate Regression   Note: Bivariate and multivariate regression are very common ways of conducting inferential statistics in political science. The readings below are meant to give you an introduction to these very important techniques.

• Reading: Massachussets Institute of Technology: Peter Dizike’s “Explained: Regression Analysis” Link: Massachussets Institute of Technology: Peter Dizike’s “Explained: Regression Analysis” (HTML)

Instructions: Watch this video about regression analysis.

• Reading: University of Delaware: John H. MacDonald’s Handbook of Biological Statistics: “Multiple Regression” Link: University of Delaware: John H. MacDonald’s Handbook of Biological Statistics: “Multiple Regression” (HTML)

6.7 Further Study Suggestions   - Reading: Statsoft: Electronic Statistics Textbook (HTML) Link: Statsoft: Electronic Statistics Textbook (HTML)

`````` Instructions: This is an optional resource.Many political
scientists who conduct empirical research rely on statisticians and
statistical resources to guide them in their collection and analysis
of the data. This site offers one such resource.

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• Reading: Rice University, University of Houston Clear Lake, and Tufts University: “Rice Virtual Lab in Statistics” Link: Rice University, University of Houston Clear Lake, and Tufts University: “Rice Virtual Lab in Statistics” (HTML)

Instructions: This is an optional resource. If you are interested in some hands-on statistical analysis of some of the central concepts discussed in the course, this is a useful site.