Lecture on Using Two-Way Tables

Introduction to Two-Way Tables

• Two-way tables are used to investigate associations between two categorical variables.
• Aim is to identify the relationship between categories e.g., cheese preference by gender.

Example Survey

• Survey Context: People surveyed for gender (male/female) and cheese preference (hard/soft cheese).
• Data Collection: Collect data points like "male, hard cheese", "female, soft cheese", and so on.

Organizing Data with Two-Way Tables

• Two-way tables simplify data interpretation compared to long lists.
• Variable Placement:
  • Explanatory variable (e.g., gender) goes on one axis.
  • Response variable (e.g., cheese preference) goes on the other.

Hypothesizing and Tallying

• Hypothesis: Gender influences cheese preference.
• Tally data to fill the table, but prefer to use a grid tallying method for clarity.

Example Tally Result

• Males: 8 like hard cheese, 4 like soft cheese.
• Females: 5 like hard cheese, 7 like soft cheese.
• Totals: Verify total counts match across axes.

Adjusting for Unequal Group Sizes

• If groups are unequal (e.g., more males surveyed), use percentages for comparison.

Calculating Column Percentages

• Ensure explanatory variable is placed correctly.
• Example Calculation:
  • Males: 8/22 for hard cheese = 36.36%
  • Females: 5/12 for hard cheese = 41.67%
• Percentages help compare preferences despite unequal group sizes.

Interpretation and Graphical Representation

• Use column graphs to visualize the data.
• Label axes, legend, and ensure accurate graph construction.
• Graph Insights:
  • Females slightly prefer hard cheese over males.
  • Both genders prefer soft cheese over hard cheese.

Expanding Beyond Two Variables

• Not limited to two categories; can include more variables.
• Example: Potato preference by educational level (boiled, mashed, chips).
• Represent data similarly with multi-category graphs.

Conclusion

• Two-way tables are powerful tools for comparing categorical data.
• Useful for visualizing and interpreting surveys and statistical relationships.