Conditional relative frequency is the proportion of cases in one group that also belong to another category, measured within a chosen row or column total of a two-way table. Joint and marginal relative frequencies describe the cell shares and row or column totals that support this calculation.
A two-way table becomes much more informative once you stop reading raw counts and start reading percentages within the relevant group.
Showing a random 20 of 50 problems.
Example 1
medium
Table: Treatment (A/B) by Outcome (Cured/Not). A: 36 cured, 12 not. B: 20 cured, 12 not. Which treatment has the higher cure rate among its own patients?Which treatment has the higher cure rate among its own patients?
Example 2
medium
Same table (M: 12 X, 18 Y; F: 21 X, 9 Y). What proportion of females chose Y?What proportion of females chose Y?
Example 3
challenge
A college reports its conditional admission rate for women is 0.40 and for men 0.50. Across two departments separately, women's rates exceed men's. What paradox is this?
Example 4
hard
In a 2x2 table, the marginal proportion of 'Yes' is 0.50. Within row 1 the conditional 'Yes' rate is 0.70. What must the within-row 'Yes' rate in row 2 be, given equal row totals?Find the missing within-row Yes rate for Row 2 given equal row totals and marginal rate 0.50
Example 5
easy
Among 50 dog owners, 20 also own a cat. What is the conditional relative frequency of cat ownership among dog owners?
Example 6
easy
Table: Studied (Yes/No) by Passed (Yes/No). Studied-Yes: 18 passed, 2 failed. What fraction of students who studied passed?Find the fraction of students who studied that passed
Example 7
hard
Conditional rates differ by row: 0.30,0.50,0.70. What does this pattern suggest about the row variable's relationship to the 'Yes' column?
Example 8
medium
In a row of totals 50, the success conditional rate is reported as 0.46. Explain why the success count must be a whole number and give it.
Example 9
medium
Table: Pet (Cat/Dog) by Likes Walks (Yes/No). Cat: 5 yes, 25 no. Dog: 35 yes, 5 no. What fraction of those who like walks are dog owners?What fraction of those who like walks are dog owners?
Example 10
medium
Why might the conditional relative frequency of 'female given chose X' differ from 'chose X given female'?
Example 11
hard
A diagnostic test has P(positive∣disease)=0.95 and P(positive∣no disease)=0.10. In a sample of 1000 with disease prevalence 5%, what is the within-column conditional rate of disease among positives?
Example 12
medium
Why might raw counts in two-way tables be misleading for comparing groups of different sizes?
Example 13
hard
In a 2x2 table the conditional rate of 'Yes' is 0.6 in row 1 and 0.6 in row 2. What does this say about an association?
Example 14
easy
Conditional relative frequency uses what number as the denominator: grand total, row/column total, or cell count?
Example 15
easy
Within a row, the conditional relative frequencies are 0.3, 0.5, and the rest. What is the last one?
Example 16
challenge
Two variables are 'independent' in a table when every conditional row distribution equals the marginal column distribution. A table has column marginals Tea =0.4, Coffee =0.6. If row N has 50 people and is independent, how many in row N prefer tea?
Example 17
medium
Table: Age (Young/Old) by Drink (Tea/Coffee). Young: 12 tea, 28 coffee. Old: 27 tea, 13 coffee. What is the tea rate among the Young?What is the tea rate among the Young?
Example 18
challenge
A 2×2 table has row totals r and 100−r. The conditional success rate is 0.8 in row 1 and 0.5 in row 2, and the overall success rate is 0.65. Find r.
Example 19
easy
Why is a conditional relative frequency different from a joint relative frequency for the same cell?
Example 20
medium
Within a row, what must the conditional relative frequencies always sum to?