Relative Risk vs Odds Ratio Flashcards: Two-Way Table Practice
Practice relative risk and odds ratio with 42 original cards on two-way tables, reference groups, odds versus probability, baseline conversions and common mistakes.
Um þennan stokk
Practice relative risk and odds ratio with 42 original cards using fictional nonclinical inspection and delivery records. Read labeled two-way tables, choose the event and reference group, and start each answer with an exact result followed by a short calculation or reason. Relative risk (risk ratio) compares event probabilities; odds ratio compares event-to-other odds. Count examples describe the recorded groups, not guaranteed population effects.
The cards practice counts → one specified risk ratio or odds ratio, a stated ratio → its meaning or relative percent change, and a local mistake → a corrected denominator, comparison or interpretation. Separate cards change the reference group or complement the event. Exact unadjusted two-probability exercises also map a baseline probability and ratio → the other probability, or identify missing or impossible information. Rare and common event examples contrast the two ratio scales without a universal approximation cutoff. Zero-boundary and inference-limit cards distinguish a finite zero from division by zero and an observed association from a causal claim or an unsupported population risk.
The sequence starts with probability and the risk-ratio scale, introduces event-to-other odds before the first odds-ratio table, then mixes arithmetic with short interpretations and repairs. Reference changes and outcome complements are introduced before baseline and boundary tasks. Broad concept families have at least three other cards between their variants. All cards use the tag risk-odds-ratios.
There are no automatic reverse copies: a ratio alone does not recover the original table or determine an absolute probability. The deck excludes rate ratios, time-to-event analysis, regression and adjusted odds ratios, confidence intervals, significance tests, automatic zero-cell corrections and clinical decisions. Outcome-selected sampling appears only as a limit on what a selected table establishes. This is introductory mathematics practice, not a complete statistics course or exam-aligned resource.
Questions, answers, explanations, organization and metadata were independently written with AI assistance. The formulas and interpretation limits were checked against Penn State STAT504 Lesson 3, sections 3.5–3.7 and STAT100 Lesson 6. All scenarios and counts are invented; no source exercises, examination questions, mark schemes, diagrams or curriculum text were copied. The cover is an original AI-generated illustration; the cards have no images.
CC0 applies to the original expression and generated cover to the extent applicable rights exist. It does not claim ownership of mathematical facts or rights in third-party material. This independent, unofficial resource is not affiliated with or endorsed by Penn State or an examination provider.
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Spjald 1
Spurning
A fictional batch contains 7 scratched panels and 21 unscratched panels. For a uniformly selected panel from this batch, what is the probability of a scratch?
Svar
1/4 (25%)
Probability uses all 28 panels: 7 ÷ (7 + 21).
Spjald 2
Spurning
In a fictional inspection record, the relative risk of a dent is 7/4 for Press A compared with Press B. Express this as a probability multiplier.
Svar
Press A’s recorded dent probability is 7/4 (1.75) times Press B’s.
The ratio compares event probabilities, with Press B as the reference.
Spjald 3
Spurning
In a fictional record, the scratch proportion is 15% for Belt A and 10% for Belt B. A learner says RR = 1.5 means A is 50 percentage points higher. What is the correct percentage-point difference?
Svar
5 percentage points
15% − 10% = 5 percentage points. The 50% increase is relative to B’s 10% baseline.
Spjald 4
Spurning
Fictional inspection counts:
Line Cracked Not cracked Cedar 9 51 Maple 6 74 For a crack, what is the relative risk (risk ratio), Cedar compared with Maple?
Svar
2
RR = (9/60) ÷ (6/80) = (3/20) ÷ (3/40). Cedar’s observed crack proportion is twice Maple’s.
Spjald 5
Spurning
A fictional batch contains 8 misprinted labels and 24 correctly printed labels. What are the odds of a misprint versus a correct print within this batch?
Svar
1/3
Odds use event count ÷ other-outcome count: 8/24. The probability would instead be 8/32.
Spjald 6
Spurning
Fictional inspection counts:
Workshop Rework needed No rework East 12 48 West 5 50 For rework versus no rework, what is the odds ratio, East compared with West?
Svar
5/2 (2.5)
OR = (12/48) ÷ (5/50) = (1/4) ÷ (1/10).
Spjald 7
Spurning
For fictional Lines A and B, the recorded odds ratio for a reject is 4, A compared with B. A learner says this alone means A’s reject probability is four times B’s. Is that interpretation valid?
Svar
No. The reject odds are four times as large.
An odds multiplier is not generally a probability multiplier; the baseline probability is needed to translate it.
Spjald 8
Spurning
Fictional counts: Scanner A flags 18 of 90 items; Scanner B flags 12 of 30. A learner divides 18 by 12 to compare flag probabilities. What is the correct risk ratio, A compared with B?
Svar
1/2 (0.5)
Use within-scanner proportions: (18/90) ÷ (12/30) = (1/5) ÷ (2/5). Raw flag counts ignore unequal totals.
Spjald 9
Spurning
A fictional bin holds 11 chipped tiles and 44 unchipped tiles. A learner calls 11/55 the odds of a chip versus no chip. What is the corrected odds value?
Svar
1/4
Use 11/44 for odds. The value 11/55 is the chip probability.
Spjald 10
Spurning
Fictional inspection counts:
Batch Smooth Rough Copper 54 18 Silver 42 7 For rough versus smooth, what is the odds ratio, Copper compared with Silver?
Svar
2
OR = (18/54) ÷ (7/42) = (1/3) ÷ (1/6). Read the outcome labels before forming the ratio.
Spjald 11
Spurning
The recorded relative risk of a barcode error is 2/5 for Printer A compared with Printer B. By what percent is A’s error probability lower?
Svar
60% lower
1 − 2/5 = 3/5 = 60%, relative to Printer B’s error probability.
Spjald 12
Spurning
Fictional counts: Machine A produces 14 rejects among 70 items; Machine B produces 5 rejects among 50. For a reject, what is the risk ratio, B compared with A?
Svar
1/2
RR = (5/50) ÷ (14/70) = (1/10) ÷ (1/5). B is the numerator group; A is the reference.
Spjald 13
Spurning
A fictional record has RR = 1 for a dent, Group A compared with Group B, and B’s dent probability is positive. What is equal between the groups?
Svar
Their recorded dent probabilities.
A ratio of 1 means the numerator and denominator probabilities are equal. It does not require equal group sizes or dent counts.
Spjald 14
Spurning
Fictional inspection counts:
Depot Delayed On time North 4 20 South 9 45 For delay versus on-time arrival, what is the odds ratio, North compared with South?
Svar
1
OR = (4/20) ÷ (9/45) = (1/5) ÷ (1/5). Different counts can give equal odds.
Spjald 15
Spurning
The recorded risk ratio for a late delivery is 9/8 for Depot A compared with Depot B. By what percent is A’s late-delivery probability higher?
Svar
12.5% higher
(9/8 − 1) × 100% = (1/8) × 100%, relative to Depot B.
Spjald 16
Spurning
Fictional inspection counts:
Outcome Robot Red Robot Blue Misaligned 6 15 Aligned 54 60 For misalignment, what is the risk ratio, Red compared with Blue?
Svar
1/2 (0.5)
RR = (6/60) ÷ (15/75) = (1/10) ÷ (1/5). Each robot’s column supplies its own total.
Spjald 17
Spurning
For fictional Groups A and B, the odds of a faulty item versus a sound item are 2/3 and 1/4, respectively. What is the odds ratio for sound versus faulty, A compared with B?
Svar
3/8
Complementing the event inverts each odds: (3/2) ÷ 4 = 3/8.
Spjald 18
Spurning
Fictional inspection counts:
Group Bent Straight B 9 45 A 12 30 For bent versus straight, what is the odds ratio, B compared with A?
Svar
1/2
OR = (9/45) ÷ (12/30) = (1/5) ÷ (2/5). The requested comparison starts with B.
Spjald 19
Spurning
Exact two-group exercise: Group B’s event probability is 1/4. The unadjusted event odds ratio is 3, Group A compared with B. What is A’s event probability?
Svar
1/2
B’s odds = (1/4)/(3/4) = 1/3. A’s odds = 3 × 1/3 = 1, so A’s probability = 1/(1 + 1).
Spjald 20
Spurning
Fictional inspection counts:
Route Damaged Undamaged Hill 5 20 Lake 12 48 For damage, what is the risk ratio, Hill compared with Lake?
Svar
1
RR = (5/25) ÷ (12/60) = (1/5) ÷ (1/5). The event proportions are equal.
Spjald 21
Spurning
In a fictional record, defect probabilities are 1/5 for Group A and 1/10 for Group B. What is the risk ratio for being defect-free, A compared with B?
Svar
8/9
The complement probabilities are 4/5 and 9/10. Their ratio is (4/5) ÷ (9/10) = 8/9.
Spjald 22
Spurning
Fictional inspection counts:
Station Loose Tight Birch 6 42 Elm 15 35 For loose versus tight, what is the odds ratio, Birch compared with Elm?
Svar
1/3
OR = (6/42) ÷ (15/35) = (1/7) ÷ (3/7).
Spjald 23
Spurning
For a fixed event, RR for Group A compared with Group B is 0: A’s event probability is 0 and B’s is positive. Does reversing the reference group give a finite risk ratio?
Svar
No. The reversed risk ratio is undefined as a finite real number.
It would divide B’s positive probability by A’s zero probability; 1/0 is not a finite value.
Spjald 24
Spurning
Exact two-group exercise: Group B’s event probability is 1/2. The unadjusted event odds ratio is 3, Group A compared with B. What is A’s event probability?
Svar
3/4
B’s odds are 1. A’s odds are 3, so A’s probability is 3/(1 + 3).
Spjald 25
Spurning
In a fictional record, pass probabilities are 3/4 for Group A and 1/2 for Group B. A learner says the failure risk ratio, A compared with B, is the reciprocal of the pass risk ratio. What is the correct failure risk ratio?
Svar
1/2
Failure probabilities are 1/4 and 1/2: (1/4) ÷ (1/2) = 1/2. Complementing the outcome does not generally reciprocate an RR.
Spjald 26
Spurning
In a fictional record, the odds ratio for a machine flag is 7/4 for Group A compared with Group B. By what percent are A’s flag odds higher?
Svar
75% higher odds
(7/4 − 1) × 100% = 75%. This is an odds comparison, not a percentage-point difference or a probability multiplier.
Spjald 27
Spurning
Exact fictional event probabilities are 3/400 in Group A and 1/400 in Group B. What is the odds ratio, A compared with B?
Svar
1197/397 (about 3.0151)
OR = (3/397) ÷ (1/399). RR = 3 is close here because both event probabilities are small; this gives no universal cutoff.
Spjald 28
Spurning
Fictional counts: Group A has 0 faulty and 16 sound items; Group B has 3 faulty and 12 sound items. For faulty versus sound, what is the odds ratio, A compared with B?
Svar
0
A’s odds are 0/16 = 0; B’s are 3/12 = 1/4. Thus OR = 0 ÷ (1/4).
Spjald 29
Spurning
Exact two-group exercise: the event probability in Group B is 3/20, and RR is 2 for Group A compared with B. What is A’s event probability?
Svar
3/10 (30%)
Multiply the reference probability by RR: 2 × 3/20.
Spjald 30
Spurning
Both groups have event probabilities strictly between 0 and 1. The event odds ratio is 5/3 for Group A compared with B. What is the non-event odds ratio for the same group comparison?
Svar
3/5
Complementing the event reciprocates each within-group odds, so it reciprocates their ratio. The stated probability bounds keep both ratios finite and nonzero.
Spjald 31
Spurning
Fictional counts:
Group Acceptable Rejected A 24 8 B 45 5 A learner uses (24 × 5)/(8 × 45) for rejected-versus-acceptable odds, A compared with B. What is the corrected odds ratio?
Svar
3
Use (8/24) ÷ (5/45) = (8 × 45)/(24 × 5) = 3. The proposed product gives the reverse comparison.
Spjald 32
Spurning
A fictional audit records every item produced by two existing lines during the same week. Line A has twice Line B’s reject proportion. Does this alone establish that using Line A causes a higher reject probability?
Svar
No. The record establishes an association for that week.
The lines may also differ in materials or other conditions. Complete recording does not remove confounding.
Spjald 33
Spurning
Fictional counts: Group A has 4 damaged items out of 20; Group B has 0 damaged out of 15. For damage, is the risk ratio A compared with B a finite real number?
Svar
No. It is undefined as a finite real number.
The calculation is (4/20) ÷ (0/15) = (1/5) ÷ 0.
Spjald 34
Spurning
An exact two-group comparison gives an event odds ratio of 2 for A compared with B, but gives no baseline probability. Can A’s event probability be determined uniquely?
Svar
No. A baseline probability is also needed.
If B’s probability is 1/3, A’s is 1/2; if B’s is 1/2, A’s is 2/3. Both pairs give OR = 2.
Spjald 35
Spurning
Exact fictional event probabilities are 9/16 in Group A and 3/16 in Group B. What is the odds ratio, A compared with B?
Svar
39/7 (about 5.5714)
OR = (9/7) ÷ (3/13) = 39/7. RR = 3, so treating OR as RR would give a substantial error here.
Spjald 36
Spurning
Fictional counts:
Group Returned Kept A 6 24 B 4 36 A learner divides (6/70) by (4/70). What is the correct risk ratio for a return, A compared with B?
Svar
2
Use each group’s total: (6/30) ÷ (4/40) = (1/5) ÷ (1/10). The grand total of 70 is not either conditional denominator.
Spjald 37
Spurning
Fictional counts: Group A has 10 flagged and 0 unflagged items; Group B has 5 flagged and 15 unflagged. For flagged versus unflagged, does ordinary division give a finite odds ratio, A compared with B?
Svar
No. A’s within-group odds already require division by zero.
A’s odds would be 10/0. Do not report a finite OR or silently add counts to the table.
Spjald 38
Spurning
Exact two-group exercise: Group B’s event probability is 3/5. Can the event risk ratio be 2 for Group A compared with B?
Svar
No. It would require an impossible probability.
A’s probability would be 2 × 3/5 = 6/5, which exceeds 1.
Spjald 39
Spurning
A fictional archive deliberately selects 40 failed items and 40 passing items, then records each item’s production line. Can within-line failure proportions in this selected table alone establish the source population’s failure risk ratio?
Svar
No. Outcome-selected counts alone do not establish the population risk ratio.
Selection fixed the failed-versus-passing mix. Population risks require further information about the sampling fractions or source counts.
Spjald 40
Spurning
In a fictional record, the odds ratio for a failed seal is 3/5 for Method A compared with Method B. By what percent are A’s failed-seal odds lower?
Svar
40% lower odds
1 − 3/5 = 2/5 = 40%. This does not say the failure probability is 40% lower.
Spjald 41
Spurning
Fictional counts: Group A has 0 late orders out of 18; Group B has 2 late orders out of 24. For lateness, what is the risk ratio, A compared with B?
Svar
0
RR = (0/18) ÷ (2/24) = 0 ÷ (1/12). A zero numerator is allowed when the reference probability is positive.
Spjald 42
Spurning
Exact two-group exercise: Group B’s event probability is 1/3. The unadjusted event odds ratio is 4, Group A compared with B. What is A’s event probability?
Svar
2/3
B’s odds are (1/3)/(2/3) = 1/2. A’s odds are 4 × 1/2 = 2, giving probability 2/(1 + 2).
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Relative Risk vs Odds Ratio Flashcards: Two-Way Table Practice
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