Analyzing Two-Way Tables for Categorical Data

Feb 11, 2025

Module 11: Two-Way Tables

Exploring the Relationship Between Two Categorical Variables

  • Objective: Understand how to explore relationships between two categorical variables.
    • Example Variables: Body image (response variable) and gender (explanatory variable).

Key Concepts

  • Comparing Distributions:

    • Compare the distribution of the response variable for different values of the explanatory variable.
    • For body image related to gender, compare body image categories between females and males.

  • Sample Distribution:

    • There are many more females than males in the sample.
    • Misleading to compare raw counts due to unequal sample sizes.

  • Using Percentages:

    • Essential to compare percentages instead of raw counts to account for different sample sizes.
    • Example Calculation:
      • Females: 560 out of 760 (73.7%) responded "about right".
      • Males: 295 out of 440 (67%) responded "about right".

Interpreting Results

  • Conditional Percentages:

    • Calculated to understand responses as if there are equal numbers of males and females (100 each).
    • Higher percentage of females feel "about right" about their body image compared to males.

  • Explanatory Variable:

    • Important to identify the explanatory variable to calculate percentages accurately.
    • Use totals for the explanatory variable for percentage calculations.

  • Conditional Distributions:

    • Females:
      • 73.7% thought their body weight was "about right".
    • Males:
      • 16.4% thought their body weight was "overweight".

  • Condition of Percentages:

    • Percentages are conditional based on being male or female.
    • Two conditional distributions are formed for comparison.

Visual Representation

  • Side-by-side display of conditional body image distributions for females and males can clearly show differences:
    • Females: 73.7% feel body weight is "about right".
    • Males: 67% feel body weight is "about right".

Summary

Understanding the relationship between categorical variables involves comparing percentages rather than raw counts, especially when sample sizes differ. Identifying and using the explanatory variable is crucial in calculating these percentages, leading to conditional distributions that can offer insights into differences between groups.