Explaining a flawed claim, then correcting it with calculations

A recurring question type: someone makes a claim based on RAW COUNTS or a simple ratio; explain WHY their reasoning is wrong, then show the correct calculation.

The two-part answer this always needs

PART 1 — EXPLAIN THE FLAW: name the SPECIFIC reasoning error — usually comparing raw counts (or a simple multiple of them) directly, without accounting for DIFFERENT GROUP SIZES.
PART 2 — CORRECT WITH CALCULATIONS: convert each raw count to a PROPORTION or RATE within its own group first, THEN compare those rates — showing the correct comparison with the actual numbers.
The conclusion should state clearly whether the original claim was right, wrong, or partially right, and by how much the true comparison actually differs from the claimed one.

Worked example Correcting a flawed "twice as likely" claim An owner claims adults are twice as likely as teenagers to order a mocha, since 76 adults and 38 teenagers ordered one (made-up figures for illustration). There are 150 teenagers and 300 adults surveyed. Explain the flaw and correct it. THE FLAW: the owner compared raw COUNTS (76 vs 38) without accounting for the fact that far more adults than teenagers were surveyed — a bigger group will naturally produce a bigger raw count even if the underlying RATE is identical. CORRECT CALCULATION: convert to rates within each group — teenagers: 38/150 ≈ 25.3%; adults: 76/300 ≈ 25.3%. COMPARE THE RATES, not the counts: both groups order mocha at almost exactly the SAME rate (≈25%), so adults are NOT twice as likely — the raw count difference is fully explained by the different sample sizes. CONCLUSION: the owner's claim is wrong — the true relative risk is close to 1, not 2. ✓ Naming the SPECIFIC flaw (comparing counts across unequal group sizes) rather than a vague "the maths is wrong" is what earns the explanation mark; the calculation must then use the ACTUAL numbers, not just gesture at the method. ✕

Correcting the calculation without ever explaining WHY the original reasoning failed

Just showing the "right" answer, with no sentence explaining what was wrong with the original reasoning (comparing counts instead of rates, or comparing groups of different sizes), only completes half of what this question type asks for — the explanation of the flaw is a separate, explicitly required part of the answer.

Answer part	What it must contain
1. Explain the flaw	Name the specific reasoning error (unequal group sizes, raw counts vs rates)
2. Correct with calculations	Convert to rates/proportions within each group, then compare
3. Conclusion	State clearly whether the claim was right, wrong, or partly right, and by how much

Practice for this standard covers the whole topic — flashcards and quiz.