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.
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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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การ์ด 1
คำถาม
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?
คำตอบ
1/4 (25%)
Probability uses all 28 panels: 7 ÷ (7 + 21).
การ์ด 2
คำถาม
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.
คำตอบ
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.
การ์ด 3
คำถาม
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?
คำตอบ
5 percentage points
15% − 10% = 5 percentage points. The 50% increase is relative to B’s 10% baseline.
การ์ด 4
คำถาม
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?
คำตอบ
2
RR = (9/60) ÷ (6/80) = (3/20) ÷ (3/40). Cedar’s observed crack proportion is twice Maple’s.
การ์ด 5
คำถาม
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?
คำตอบ
1/3
Odds use event count ÷ other-outcome count: 8/24. The probability would instead be 8/32.
การ์ด 6
คำถาม
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?
คำตอบ
5/2 (2.5)
OR = (12/48) ÷ (5/50) = (1/4) ÷ (1/10).
การ์ด 7
คำถาม
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?
คำตอบ
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.
การ์ด 8
คำถาม
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?
คำตอบ
1/2 (0.5)
Use within-scanner proportions: (18/90) ÷ (12/30) = (1/5) ÷ (2/5). Raw flag counts ignore unequal totals.
การ์ด 9
คำถาม
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?
คำตอบ
1/4
Use 11/44 for odds. The value 11/55 is the chip probability.
การ์ด 10
คำถาม
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?
คำตอบ
2
OR = (18/54) ÷ (7/42) = (1/3) ÷ (1/6). Read the outcome labels before forming the ratio.
การ์ด 11
คำถาม
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?
คำตอบ
60% lower
1 − 2/5 = 3/5 = 60%, relative to Printer B’s error probability.
การ์ด 12
คำถาม
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?
คำตอบ
1/2
RR = (5/50) ÷ (14/70) = (1/10) ÷ (1/5). B is the numerator group; A is the reference.
การ์ด 13
คำถาม
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?
คำตอบ
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.
การ์ด 14
คำถาม
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?
คำตอบ
1
OR = (4/20) ÷ (9/45) = (1/5) ÷ (1/5). Different counts can give equal odds.
การ์ด 15
คำถาม
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?
คำตอบ
12.5% higher
(9/8 − 1) × 100% = (1/8) × 100%, relative to Depot B.
การ์ด 16
คำถาม
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?
คำตอบ
1/2 (0.5)
RR = (6/60) ÷ (15/75) = (1/10) ÷ (1/5). Each robot’s column supplies its own total.
การ์ด 17
คำถาม
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?
คำตอบ
3/8
Complementing the event inverts each odds: (3/2) ÷ 4 = 3/8.
การ์ด 18
คำถาม
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?
คำตอบ
1/2
OR = (9/45) ÷ (12/30) = (1/5) ÷ (2/5). The requested comparison starts with B.
การ์ด 19
คำถาม
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?
คำตอบ
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).
การ์ด 20
คำถาม
Fictional inspection counts:
Route Damaged Undamaged Hill 5 20 Lake 12 48 For damage, what is the risk ratio, Hill compared with Lake?
คำตอบ
1
RR = (5/25) ÷ (12/60) = (1/5) ÷ (1/5). The event proportions are equal.
การ์ด 21
คำถาม
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?
คำตอบ
8/9
The complement probabilities are 4/5 and 9/10. Their ratio is (4/5) ÷ (9/10) = 8/9.
การ์ด 22
คำถาม
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?
คำตอบ
1/3
OR = (6/42) ÷ (15/35) = (1/7) ÷ (3/7).
การ์ด 23
คำถาม
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?
คำตอบ
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.
การ์ด 24
คำถาม
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?
คำตอบ
3/4
B’s odds are 1. A’s odds are 3, so A’s probability is 3/(1 + 3).
การ์ด 25
คำถาม
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?
คำตอบ
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.
การ์ด 26
คำถาม
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?
คำตอบ
75% higher odds
(7/4 − 1) × 100% = 75%. This is an odds comparison, not a percentage-point difference or a probability multiplier.
การ์ด 27
คำถาม
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?
คำตอบ
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.
การ์ด 28
คำถาม
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?
คำตอบ
0
A’s odds are 0/16 = 0; B’s are 3/12 = 1/4. Thus OR = 0 ÷ (1/4).
การ์ด 29
คำถาม
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?
คำตอบ
3/10 (30%)
Multiply the reference probability by RR: 2 × 3/20.
การ์ด 30
คำถาม
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?
คำตอบ
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.
การ์ด 31
คำถาม
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?
คำตอบ
3
Use (8/24) ÷ (5/45) = (8 × 45)/(24 × 5) = 3. The proposed product gives the reverse comparison.
การ์ด 32
คำถาม
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?
คำตอบ
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.
การ์ด 33
คำถาม
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?
คำตอบ
No. It is undefined as a finite real number.
The calculation is (4/20) ÷ (0/15) = (1/5) ÷ 0.
การ์ด 34
คำถาม
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?
คำตอบ
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.
การ์ด 35
คำถาม
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?
คำตอบ
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.
การ์ด 36
คำถาม
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?
คำตอบ
2
Use each group’s total: (6/30) ÷ (4/40) = (1/5) ÷ (1/10). The grand total of 70 is not either conditional denominator.
การ์ด 37
คำถาม
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?
คำตอบ
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.
การ์ด 38
คำถาม
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?
คำตอบ
No. It would require an impossible probability.
A’s probability would be 2 × 3/5 = 6/5, which exceeds 1.
การ์ด 39
คำถาม
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?
คำตอบ
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.
การ์ด 40
คำถาม
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?
คำตอบ
40% lower odds
1 − 3/5 = 2/5 = 40%. This does not say the failure probability is 40% lower.
การ์ด 41
คำถาม
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?
คำตอบ
0
RR = (0/18) ÷ (2/24) = 0 ÷ (1/12). A zero numerator is allowed when the reference probability is positive.
การ์ด 42
คำถาม
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?
คำตอบ
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).
42 การ์ด
Relative Risk vs Odds Ratio Flashcards: Two-Way Table Practice
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