Overview
This lecture introduces the analysis of two categorical variables using contingency tables, focusing on calculating and interpreting marginal and joint percentages.
Introduction to Two Categorical Variables
- Analyzing two categorical variables involves studying their relationship and calculating key statistics.
- Questions can be about preferences (e.g., social media) and binary traits (e.g., having a tattoo or not).
Contingency Table (Two-Way Table)
- A contingency table summarizes counts of all combinations for two categorical variables.
- Rows and columns represent different categories of each variable; totals are included for each.
- The bottom-right corner shows the "grand total" of all responses.
- Table size is counted as number of rows (excluding totals) by number of columns (excluding totals).
- The structure (e.g., 5 by 2) depends on the arrangement of variables, not including totals.
Reading a Contingency Table
- Each cell represents the count for a specific combination (e.g., Instagram users with tattoos).
- Row and column totals summarize responses for each category.
- Grand total equals both the sum of all row totals and the sum of all column totals.
Marginal Percentages (Marginal Probability/Proportion)
- Marginal percentage concerns only one variable, regardless of the other.
- Calculated as the category total divided by the grand total (e.g., students with tattoos divided by all students).
- Use the term "of all the students" to identify when to use the grand total.
- Percentage = (category total / grand total) × 100, rounded to the tenths place.
Calculating Proportions and Percentages
- Proportion is the decimal equivalent of a percentage; round to three decimal places.
- To convert a proportion to a percentage, multiply by 100%.
- Example: 85 tattooed students out of 326 total = 0.261 (rounded), or 26.1%.
Key Terms & Definitions
- Categorical variable — a variable with values that are categories, not numbers.
- Contingency table — a table showing counts for all category combinations of two variables.
- Grand total — the total number of observations in the table.
- Marginal percentage/probability/proportion — percentage for one variable, ignoring the other.
- Proportion — decimal form of a percentage.
- Two-way table — another term for contingency table.
Action Items / Next Steps
- Practice identifying marginal percentages in contingency tables.
- Prepare for next lecture on calculating and interpreting joint (or intersecting) percentages.