Unit 2, Lesson 2 : Statistics for Categorical Variables
Statistics for Categorical Variables
Unit 2, Topic 2.3: Statistics for Categorical Variables
Overview
This lesson builds on two-way tables by calculating marginal and conditional relative frequencies to compare distributions and spot associations between two categorical variables (like gender and sport preference). Marginal frequencies show row or column totals as proportions of the whole. Conditional frequencies show cell values as proportions within a row or column. Context, like who the data is from, matters because it explains associations (e.g., more soccer for males in a teen survey might link to team sports).
These calculations help assess if variables are related or if patterns are chance. We’ll use side-by-side bar graphs for comparisons and justify claims.
Assignment:
Part 1: Guided Practice Activity
Work on your own. Use the two-way table below from 20 students (from a class survey). Calculate marginal and conditional frequencies, then compare.
Two-Way Table (Frequencies):
| Gender | Soccer | Basketball | Tennis | Row Total |
|---|---|---|---|---|
| Male | 6 | 3 | 3 | 12 |
| Female | 3 | 2 | 3 | 8 |
| Column Total | 9 | 5 | 6 | 20 |
Tasks:
- Calculating Marginal Frequencies:
- Calculate row marginal relative frequencies (row total / overall total, e.g., Male: 12/20 = 0.6).
- Calculate column marginal relative frequencies (column total / overall total, e.g., Soccer: 9/20 = 0.45).
- Write 1-2 sentences about distributions (e.g., "Males are 60% of the group, showing more males overall.").
- Extra Practice: For a new table (e.g., "Pet: Dog/Cat" rows, "Age Group: Teen/Adult" columns), calculate marginals.
- Determining Conditional Frequencies:
- Calculate row conditional relative frequencies (cell / row total, e.g., Soccer given Male: 6/12 = 0.5).
- Calculate column conditional relative frequencies (cell / column total, e.g., Male given Soccer: 6/9 ≈ 0.67).
- Write 1-2 sentences assessing associations (e.g., "50% of males prefer soccer, higher than females' 37.5%, suggesting a link.").
- Extra Practice: Calculate conditionals for your "Pet" table and note associations.
- Reflection:
- Sketch a side-by-side bar graph (bars for sports by gender, heights for conditionals).
- Write 2-3 sentences comparing distributions and justifying a claim with context (e.g., "Side-by-side bars show males favor soccer more; in teens, this might link to school teams.").
Part 2: Independent Practice
Use this two-way table from 16 students:
| Exercise Level | Water | Soda | Column Total |
|---|---|---|---|
| High | 8 | 3 | 11 |
| Low | 2 | 3 | 5 |
| Row Total | 10 | 6 | 16 |
Tasks:
- Calculate all marginal relative frequencies (row and column).
- Calculate all conditional relative frequencies (row and column).
- Sketch a side-by-side bar graph using conditionals (e.g., bars for drinks by exercise level).
- Write 2-3 sentences comparing distributions, assessing associations, and justifying a claim with context (e.g., "80% of high exercisers choose water conditionally, suggesting health ties in active students.").
- Extra Activity: Invent a two-way table (e.g., "Study Group: Yes/No" and "Pass/Fail"). Calculate marginals/conditionals, sketch bars, and claim with context.
Homework Assignment
- Collect data from 5 people on two categorical variables (e.g., "Coffee: Yes/No" and "Alertness: High/Low"). Make a two-way table, calculate marginal and conditional frequencies, sketch a side-by-side bar graph, compare distributions, and justify a claim with context to share next class.