Statistics

Fundamentals of Social Statistics

Adam J. McKee


This is my OER guide to very basic concepts of basic social statistics.  Note that this is not designed to be a comprehensive text for graduate students.  My bent is decidedly conceptual, and my goals tend toward intelligent consumerism that computational proficiency.  Rather than doing computations “by hand,” I focus on doing things in Excel or similar spreadsheet programs (e.g., Google Sheets).


This work is licensed under an Open Educational Resource-Quality Master Source (OER-QMS) License.

Open Education Resource--Quality Master Source License


Table of Contents

Preface


Section 1:  Basic Concepts

Section 1.1:  Statistics and the Social Sciences


Section 1.2:  Basic Math Review


Section 1.3:  Using Spreadsheets


Section 1.4: Variables


Section 1.5:  Scales of Measurement


Chapter 2:  Collecting and Organizing Data

Section 2.1: Probability and Samples


Section 2.2:  Nonprobability Sampling


Section 2.3: Describing Data


Section 2.4:  Percentages & Rates


Section 2.5:  Frequency Distributions


Chapter 3:  Describing Variables

Section 3.1:  Measures of Central Tendency


Section 3.2:  Measures of Variability


Section 3.3:  Standard Deviation


Section 3.4:  The Normal Curve


Section 3.5:  Percentiles and Standard Scores


Chapter 4:  Exploring Relationships

Section 4.1:  Introduction to Effect Size


Section 4.2:  Correlation


Section 4.3: Multiple Correlations


Section 4.4:  Linear Regression


Section 4.5: Advanced Regression Models


Chapter 5:  Hypothesis Testing

Section 5.1:  The Logic of Hypothesis Testing


Section 5.2:  Decision Errors


Section 5.3: Power


Section 5.4: Assumptions

  • Common Assumptions

Section 5.5: One-tailed vs. Two-tailed Tests


Chapter 6: Testing Null Hypotheses

Section 6.1: Error and Confidence Intervals


Section 6.2: t-Tests

  • t-Test for Independent Groups
  • t-Test for Independent Groups in Excel
  • t-Test for Dependent Groups
  • t-Tests with Effect Size
  • Computing d and r In Excel
  • Computing a Dependent Sample t-Test in Excel

Section 6.3: Non-parametric Tests

  • Chi-square
  • Computing Chi-square Probability with Excel

Section 6.4:  Significance and Correlations


Section 6.5:  ANOVA Tests

  • Post Hoc Tests
  • Computing the Probability of F in Excel
  • Post Hoc tests
  • Tukey’s Test
  • Two-Way ANOVA Tests

Chapter 7: Complex Models

Section 7.1: Multiple Regression

  • What Are Linear Models?
  • Interpreting Regression Results
  • Running a Multiple Regression in Excel
  • Examining Data
  • Transforming Data
  • Statistical Inference and Regression
  • Variance Partitioning
  • Hierarchical Regression Analysis
  • Analysis of Effects

Section 7.2: Factor Analysis

  • Higher Order Factors
  • How Much Does A Factor Explain?
  • Assessing Individual Variables
  • Types of Factor Analytic Techniques
  • Problems to Watch For

Section 7.3:  Logistic Regression

  • Why can’t we use regular (OLS) Regression?
  • About the Distributions
  • About Odds Ratios
  • How are they Different?

Section 7.4: ANCOVA


Section 7.5: Structural Equation Models (SEMs)

  • Simple Models
  • Variable Types
  • Simple Regression
  • Identification
  • Types of Effects
  • Model Testing
  • Latent Variables
  • Path Coefficients
  • Correlated Error Terms
  • Models

Appendix A:  Significance of Pearson’s r


Appendix B: Critical Values of ChChi-Square


Appendix C:  Critical Values for Student’s t


Appendix D:  Critical Values of F (.05 Level)


Appendix E: Studentized Range Statistic (q)


Appendix F: Standard Normal Distribution Table


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Last Modified:  06/28/2018