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