chapter 10

NUMBERING RACE LECTURE NOTES

Overview

  • Lecture Title: Bivariate Tables

  • Instructor: Nneka Ibekwe-Okafor, PhD

  • Institution: The University of Texas at Austin

Course Resources

  • Lecture Tools: Live engagement through web polls at Pollev.com/niokafor

Academic Schedule

  • Week 1-16 Class Topics and Assignments:

    • August 25: Course Introduction

    • September 1: No Class (Labor Day)

    • September 3: Analytic Software Introduction (PS1 Due 9/5)

    • September 8: Topics spanning research, central tendency, variability, distributions, hypothesis testing, and bivariate tables

    • Example Dates and Topics:

      • October 15: Bivariate Tables

      • December 3: Lab and Final Assignment due

Lecture Agenda

  • Chapter 8: Testing Hypotheses

    • Stating the Research and Null Hypotheses

  • Chapter 9: Bivariate Tables

    • Creating and analyzing a bivariate table

    • Identifying properties of a bivariate table

    • Describing Relationships Between Variables

Hypothesis Testing Overview

  • Purpose of Hypothesis Testing:

    • To determine if the null hypothesis can be rejected or approved.

    • Null Hypothesis (H0): There is no difference, no effect, or no relationship between variables.

    • If rejected, the research hypothesis (H1) can be accepted; if accepted, H1 is rejected.

Research Process Steps

  1. Develop Research Design

  2. Contribute New Evidence to Literature

  3. Asking Research Questions

  4. Formulating Hypotheses

  5. Evaluating Hypotheses

  6. Analyzing Data

  7. Collecting Data

Notations in Sampling and Populations

  • Sample Notation | Population Notation

    • Mean: $Y$ | $bc$

    • Proportion: $p$ | $c0$

    • Standard Deviation: $s$ | $c3$

    • Variance: $s^2$ | $c3^2$

Basic Hypothesis Testing Notations

  • Research Hypotheses:

    • H0: No relationship

    • H1: Some relationship exists

Types of Errors in Hypothesis Testing

  • Type I Error (False Positive): Rejecting a true null hypothesis.

  • Type II Error (False Negative): Failing to reject a false null hypothesis.

Bivariate Analysis Introduction

  • Definition: Analysis of two variables to determine relationships between them.

  • Dependent Variable: Outcome or effect.

  • Independent Variable: Predictor or cause.

Variable Types

  1. Categorical Variables: Nominal, Ordinal

  2. Numeric Variables: Continuous (Interval, Ratio), Discrete (Interval, Ratio)

Bivariate Tables

  • Definition: Cross-tabulation technique for analyzing the relationship between two variables organized in a table format.

    • Example: Race Category vs. Home Ownership Status

    • Data Example: | Race | Home Ownership | Frequency | | ---- | -------------- | -------- | | Black | Yes | 50 | | Black | No | 50 | | White | Yes | 10 | | White | No | 40 |

      • Total (N): 100

Constructing Bivariate Tables

  • Features:

    • Rows: Dependent variable

    • Columns: Independent variable

    • Cell frequencies: Distribution of observations

    • Marginal totals: Total for each category

  • Table Types: r x c (e.g., 2 x 2, 3 x 2)

Example of Bivariate Table Construction by Hand

  • Table Type: 3 x 2 (3 rows and 2 columns)

Excel Example: Steps to Construct a Bivariate Table

  1. Highlight data for the two variables in Excel.

  2. Select "Insert" -> "Pivot Table".

  3. Choose the location for the table.

  4. Drag independent variable (e.g., race) to the column area.

  5. Drag dependent variable (e.g., home ownership) to the row area.

  6. Calculate frequencies and percentages as needed.

Analysis of Bivariate Relationships

  • Properties Include:

    • Existence: Determine if a relationship appears.

    • Strength: Analyze the percentage differences across categories; classified as weak, moderate, or strong.

    • Direction: Discuss when applicable (mostly with ordinal data).

Understanding Percentages in Bivariate Analysis

  • Percentage vs. Percentage Points:

    • Percentage Difference: Comparing how much something relates to 100.

    • Percentage Points Difference: The absolute difference between two percentages.

Examples of Strength Assessments

  • Assessment: Moderate strength indicated by a 31% difference in home ownership rates between racial groups.

Practical Application of Race Variable in Research

  • Ethical Considerations:

    • Race and inequality should be contextualized as social constructs.

    • Assessing disparities should avoid perpetuating harmful stereotypes.

Elaboration of Relationships

  • Concept: The process of exploring bivariate relationships further with control variables to test for nonspuriousness and to establish clear causal links.

  • Direct vs. Spurious Relationships: A clear outcome linked directly to the independent variable versus a false impression of causation due to unaccounted factors.

Final Thoughts and Future Considerations

  • Recognize the importance of controlling variables when analyzing bivariate relationships.

  • Continually revisit assumptions and contexts around variables, particularly socially constructed categories like race.

Exam II Overview

  • 50 questions from chapters on hypothesis testing and bivariate tables, allowing 3 pages of notes.

  • Attendance will be taken, and no internet use permitted during the exam.

Contact Information

  • Instructor Email: niokafor@utexas.edu