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


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