L4.3: Association between two categorical variables - Relative frequencies

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Learning outcomes

• compute relative frequencies in a two-way table
• distinguish row percentages from column percentages
• compare groups fairly when totals differ
• interpret association using proportions rather than only counts

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Why relative frequencies matter

• When groups have different sizes, raw counts may be unfair for comparison.
• Relative frequencies convert counts into comparable proportions.

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Row relative frequencies

• Divide each cell by its row total.
• Useful when comparing distribution within each row group.

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Column relative frequencies

• Divide each cell by its column total.
• Useful when comparing distribution within each column group.

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Example idea

• what fraction of this group falls in each category?

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Interpretation

• If row percentages are very similar across rows, association may be weak.
• If row percentages differ strongly, association may be stronger.

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Exam hints and traps

• Always state whether percentages are row-based or column-based.
• Relative frequency is proportion, not count.
• Percentages in one row should total 100% if row percentages are used.
• Use comparable percentages before making claims.

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Quick practice

1. Why are row percentages useful?
2. In row-relative frequencies, what should each row sum to?
3. When should raw count comparison be avoided?

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Answer key

1. They compare category share within each row group
2. 100%
3. When group totals differ greatly