Exploring Bivariate Analysis and Hypothesis Testing

Sep 11, 2024

Lecture Notes: Sociology Through Statistics - Bivariate Analysis and Hypothesis Writing

Introduction

  • Instructor: Dr. Alvarez
  • Course Focus: Bivariate Analysis and Hypothesis Writing
  • Objective of Current Section: Understanding relationships between two variables and writing/testing hypotheses.

Course Recap

  • Unit 1: Research Methods
    • Induction, Deduction
    • Conceptualization
  • Unit 2: Sampling Techniques
    • Difference between probability and non-probability samples
  • Unit 3: Introduction to SPSS
  • Unit 4: Univariate Descriptive Statistics
    • Tools: Frequency table, Measures of central tendency, Measures of dispersion

Bivariate Analysis

  • Focus: Relationships between two variables (Independent and Dependent)
  • Objective: Determine if there is a correlation between the variables.
  • Examples: Human Capital Theory (Education and Income)
  • Variables:
    • X Variable: Independent
    • Y Variable: Dependent

Key Concepts

  • Covariation: Establish if two variables covary in a meaningful way
  • Tools for Bivariate Analysis:
    • Crosstabs
    • Comparisons of Means
    • Correlation Coefficient (later in the course)
  • Sample Context: GSS 2014 (General Social Survey) as an example

Writing Hypotheses

  • Deductive Methods: Start with a theory or hypothesis, then evaluate data.
  • Types of Hypotheses:
    • Research Hypothesis: Proposed relationship/expectation between variables.
    • Null Hypothesis: No relationship between the variables.
  • Importance: Hypotheses guide the research design and evaluation process.

Testing Hypotheses

  • Statistical Significance: Indicates real relationships exist beyond sample chance
  • Inference: Evaluate if sample relationships hold in the wider population
  • Steps:
    1. Test for Statistical Significance
    2. Evaluate Hypotheses

Types of Bivariate Analysis

  • Crosstabs: Used for nominal/ordinal dependent variables regardless of the independent variable
  • Comparison of Means: Used for interval/ratio dependent and nominal/ordinal independent variables
  • Correlation & Regression: For interval/ratio dependent and independent variables

Statistical Significance Tests

  • Crosstabs: Inferential test is Chi-Square
  • Comparison of Means: Tests are t-test and ANOVA
  • Correlation & Regression: Use F-tests and t-tests
  • P-Value: Probability measure to determine significance (significant if < 0.05)

Hypotheses Writing and Evaluation

  • Good Hypotheses:
    • Include direction (positive or negative relationships)
    • Compare categories for nominal variables
  • Positive Relationships: Variables move in the same direction
  • Negative Relationships: Variables move in opposite directions

Evaluating Hypotheses

  • Null Hypothesis: Rejected if p-value < 0.05
  • Research Hypothesis: Supported if analysis shows expected variable relationship

Conclusions

  • Key Tasks: Look at SPSS output, describe and interpret bivariate analyses, and determine statistical significance.
  • Overall Goal: Understand relationships and infer population patterns from sample data.