Biostatistics Quiz: Sensitivity Specificity Ppv And Npv
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Sensitivity Specificity Ppv And NpvQuestion 1 of 20

A diagnostic test correctly identifies 180 of 200 patients with disease (true positives) and correctly identifies 760 of 800 patients without disease (true negatives). If this test is applied to a new population where the disease prevalence is 25%, what will be the negative predictive value?

Approximately 94.1%
Approximately 95.0%
Approximately 90.0%
Approximately 96.6%
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Biostatistics Quiz

Biostatistics Quiz: Sensitivity Specificity Ppv And Npv

Practice Sensitivity Specificity Ppv And Npv in Biostatistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Sensitivity Specificity Ppv And Npv, giving you a quick way to practice the rules, question types, and explanations that matter most for Biostatistics.

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Question 1

A diagnostic test correctly identifies 180 of 200 patients with disease (true positives) and correctly identifies 760 of 800 patients without disease (true negatives). If this test is applied to a new population where the disease prevalence is 25%, what will be the negative predictive value?

  1. Approximately 94.1%
  2. Approximately 95.0%
  3. Approximately 90.0%
  4. Approximately 96.6% (correct answer)
Explanation: First calculate test characteristics: Sensitivity = 180/200 = 90%, Specificity = 760/800 = 95%. Then calculate NPV for 25% prevalence: NPV = (0.95 × 0.75) / [(0.10 × 0.25) + (0.95 × 0.75)] = 0.7125 / (0.025 + 0.7125) = 0.7125 / 0.7375 ≈ 0.966 or 96.6%. Choice A represents a calculation error. Choice B incorrectly uses specificity directly. Choice C incorrectly uses sensitivity directly.

Question 2

A point-of-care test has sensitivity of 75% and specificity of 88%. A physician uses this test in two different populations: Population A (prevalence 30%) and Population B (prevalence 3%). How do the negative predictive values compare between these populations?

  1. NPV is approximately 15 percentage points higher in Population B than Population A
  2. NPV is approximately equal in both populations since sensitivity remains constant
  3. NPV is approximately 5 percentage points higher in Population A than Population B
  4. NPV is approximately 10 percentage points higher in Population B than Population A (correct answer)
Explanation: When you encounter questions about predictive values across different populations, remember that negative predictive value (NPV) depends heavily on disease prevalence, even when test characteristics remain constant. Let's calculate the NPV for both populations using the given sensitivity (75%) and specificity (88%). NPV equals true negatives divided by all negative test results. For Population A (30% prevalence):
  • In 1000 people: 300 have disease, 700 don't
  • True negatives: 700 × 0.88 = 616
  • False negatives: 300 × 0.25 = 75
  • Total negative tests: 616 + 75 = 691
  • NPV = 616/691 = 89.1%
For Population B (3% prevalence):
  • In 1000 people: 30 have disease, 970 don't
  • True negatives: 970 × 0.88 = 853.6
  • False negatives: 30 × 0.25 = 7.5
  • Total negative tests: 853.6 + 7.5 = 861.1
  • NPV = 853.6/861.1 = 99.1%
Population B has an NPV approximately 10 percentage points higher than Population A, confirming answer D. Answer A overstates the difference (15 vs. actual 10 percentage points). Answer B incorrectly assumes NPV stays constant—this confuses sensitivity with NPV. Answer C gets the direction wrong, claiming Population A has higher NPV when it's actually lower. Remember: NPV increases as prevalence decreases because there are fewer false negatives relative to true negatives. In low-prevalence populations, negative tests are more reliable for ruling out disease.

Question 3

A test has sensitivity 90%, specificity 70%, prevalence 20%. What is the PPV?

  1. 43% (correct answer)
  2. 56%
  3. 24%
  4. 75%
Explanation: In 1,000 people, 200 have the disease and 90% sensitivity gives 180 true positives. Of 800 without disease, 30% test positive, giving 240 false positives. PPV = 180 divided by (180 + 240) = 43%. The tempting error is using sensitivity 90% directly, which ignores false positives and disease prevalence.

Question 4

A test has 80% sensitivity, 95% specificity, and 10% prevalence. What is the NPV?

  1. 80%
  2. 99%
  3. 90%
  4. 98% (correct answer)
Explanation: In 1,000 people, 100 have the disease and 900 do not. Sensitivity 80% means 20 infected people test negative, while specificity 95% gives 855 true negatives among healthy people. NPV is 855 divided by 855 + 20, or 855/875, which is 97.7%, about 98%. The tempting 99% is wrong because it overlooks the 20% of diseased patients who falsely test negative.

Question 5

Assuming independent repeats, requiring two positive results instead of one changes sensitivity and specificity how?

  1. Sens increases; Spec decreases
  2. Sens decreases; Spec increases (correct answer)
  3. Sens increases; Spec increases
  4. Sens decreases; Spec decreases
Explanation: Requiring two positives makes the overall test harder to call positive. Sensitivity is the chance a diseased person tests positive, so it becomes sensitivity squared and falls. Specificity is the chance a healthy person tests negative; with two tests it rises because both false positives are needed to be wrong. The tempting error is thinking extra testing increases both sensitivity and specificity, but sensitivity suffers under a stricter positive rule.

Question 6

A test has 95% sensitivity and 90% specificity; prevalence is 1%. Given a positive test, the result is most likely:

  1. A false positive (correct answer)
  2. A true positive
  3. A false negative
  4. A true negative
Explanation: With 1% prevalence, 990 of 1,000 people are disease-free. At 90% specificity, 10% of those 990, or 99, are false positives, while only 9.5 of the 10 diseased people are true positives. So most positive results are false positives. The tempting answer is true positive, but that ignores how low prevalence makes false positives outnumber true positives.

Question 7

If prevalence falls while sensitivity and specificity are unchanged, what happens to PPV and NPV?

  1. PPV and NPV both decrease
  2. PPV increases; NPV decreases
  3. PPV decreases; NPV increases (correct answer)
  4. PPV and NPV both increase
Explanation: With fewer people truly having the disease, a positive result is more likely to be a false positive, so PPV falls. At the same time, a negative result is more likely to be a true negative because the disease is rarer, so NPV rises. The tempting error is thinking both predictive values move together, but they move in opposite directions when prevalence changes.

Question 8

A meta-analysis reports that a diagnostic test has a sensitivity of 88% (95% CI: 82%-94%) and specificity of 91% (95% CI: 87%-95%). A clinician wants to counsel patients about test performance in her practice where disease prevalence is 18%. What is the most appropriate statement about the positive predictive value?

  1. The PPV will be exactly 88% matching the reported sensitivity
  2. The PPV will be approximately 70% with range 60-78% (correct answer)
  3. The PPV will be exactly 91% matching the reported specificity
  4. The PPV cannot be determined from the given information
Explanation: Using point estimates: PPV = (0.88 × 0.18) / [(0.88 × 0.18) + (0.09 × 0.82)] = 0.1584 / 0.2322 ≈ 68%. Using confidence intervals: worst case (82% sensitivity, 87% specificity) gives PPV ≈ 58%, best case (94% sensitivity, 95% specificity) gives PPV ≈ 77%. Choice A confuses sensitivity with PPV. Choice C confuses specificity with PPV. Choice D incorrectly suggests insufficient information is provided.

Question 9

Prevalence is 10%; sensitivity 90%, specificity 80%. Probability a positive result has the disease?

  1. About 33% (correct answer)
  2. About 25%
  3. About 50%
  4. About 90%
Explanation: Out of 100 people, 10 have disease; 9 test positive. 90 without disease; 20% false positive means 18 positive tests. So positive results total 27, of whom 9 truly have disease: 9/27 = 33%. The tempting 90% confuses sensitivity with predictive value; it ignores that most tested people are healthy.

Question 10

Lowering a test's cutoff raises sensitivity. What happens to the false-positive rate?

  1. It will increase (correct answer)
  2. It will decrease
  3. It remains constant
  4. Depends on prevalence
Explanation: Lowering the cutoff makes more test results fall into the positive side. You pick up more true cases, which is why sensitivity rises, but you also flag more healthy people as positive, so the false-positive rate increases. The tempting wrong answer is that it decreases, but that confuses false positives with false negatives; false negatives fall, false positives rise.

Question 11

Disease prevalence rises from 5% to 20% with sensitivity and specificity unchanged. What happens to predictive values?

  1. PPV falls; NPV falls
  2. PPV falls; NPV rises
  3. PPV rises; NPV rises
  4. PPV rises; NPV falls (correct answer)
Explanation: When disease becomes more common, a positive result is more likely to be a true positive, so PPV rises. At the same time, with more disease in the population, a negative result leaves more real disease among those who test negative, so NPV falls. The tempting error is thinking rising prevalence makes positives less reliable, but prevalence raises the prior probability of disease before testing.

Question 12

A test has 95% sensitivity and 92% specificity. In 200 healthy people, how many positive tests are expected?

  1. About 8
  2. About 10
  3. About 16 (correct answer)
  4. About 184
Explanation: With 92% specificity, 92% of 200 healthy people are correctly negative: 184 people. That leaves 200 - 184 = 16 healthy people expected to test positive as false positives. The tempting error is 184, but that's the number expected to test negative, not positive.

Question 13

Prevalence is 1%; sensitivity and specificity are each 90%. Chance a negative test is truly disease-free?

  1. About 90.0%
  2. About 99.9% (correct answer)
  3. About 99.0%
  4. About 8.3%
Explanation: Out of 10,000 people, 100 have disease and 9,900 do not. Of the 100 diseased, 10 test negative. Of the 9,900 disease-free, 8,910 test negative. So negative tests total 8,920, and 8,910 are truly disease-free: 8,910 / 8,920 = about 99.9%. The tempting 90% is just the specificity, but it ignores that negative results are mostly from the large disease-free group.

Question 14

A research team develops a diagnostic algorithm with 92% sensitivity and 85% specificity. They want to minimize false negative results even if it means accepting more false positives. Which modification would best achieve this goal while maintaining the same underlying test characteristics?

  1. Lower the decision threshold to increase sensitivity to 96% and decrease specificity to 75% (correct answer)
  2. Raise the decision threshold to increase specificity to 92% and decrease sensitivity to 85%
  3. Use the test only in high-prevalence populations where PPV will be maximized
  4. Use the test only in low-prevalence populations where NPV will be maximized
Explanation: To minimize false negatives, sensitivity must be increased, which typically requires lowering the decision threshold. This trade-off decreases specificity (more false positives) but achieves the stated goal of fewer false negatives. Choice B increases false negatives by lowering sensitivity. Choice C addresses PPV but doesn't change the test's sensitivity. Choice D maximizes NPV but doesn't specifically target reducing false negatives through threshold adjustment.

Question 15

A screening mammogram has 90% sensitivity and 85% specificity for detecting breast cancer. In a population where 2% of women have breast cancer, what percentage of women with negative mammograms actually do NOT have cancer?

  1. Approximately 98.8%
  2. Approximately 99.8% (correct answer)
  3. Approximately 85.0%
  4. Approximately 90.0%
Explanation: This asks for NPV. NPV = (Specificity × (1-Prevalence)) / [(1-Sensitivity) × Prevalence + Specificity × (1-Prevalence)] = (0.85 × 0.98) / [(0.10 × 0.02) + (0.85 × 0.98)] = 0.833 / (0.002 + 0.833) = 0.833 / 0.835 ≈ 0.998 or 99.8%. Choice A incorrectly uses (1-Prevalence) directly. Choice C incorrectly uses specificity. Choice D incorrectly uses sensitivity.

Question 16

A diagnostic test has PPV = 60% and NPV = 95% in a population with 8% disease prevalence. What is the specificity of this test?

  1. 88.3%
  2. 91.7%
  3. 94.2%
  4. 96.8% (correct answer)
  5. 98.1%
Explanation: When you encounter diagnostic test questions involving PPV, NPV, and prevalence, you need to work backwards from these summary statistics to find the underlying test characteristics like sensitivity and specificity. Start by setting up what you know. With 8% prevalence, imagine 1000 people: 80 have disease, 920 don't. Since NPV = 95%, among all negative tests, 95% are true negatives. Let's say there are X positive tests, so (1000-X) negative tests. From NPV: true negatives = 0.95(1000-X), and true negatives also equal (920 - false positives). Since PPV = 60%, among X positive tests, 60% are true positives: 0.6X = true positives. But true positives also equal (80 - false negatives). Setting up the equations: 0.95(1000-X) = 920 - (X - 0.6X), which simplifies to find X = 67 positive tests. This gives us 33 false positives (67 - 40 true positives) and 887 true negatives. Specificity = true negatives/(true negatives + false positives) = 887/(887 + 33) = 887/920 = 96.5%, closest to answer D) 96.8%. The other answers represent common calculation errors: A) 88.3% likely confuses sensitivity with specificity calculations, B) 91.7% might result from incorrectly handling the prevalence adjustment, and C) 94.2% could come from using NPV directly without proper conversion. Remember: when working with PPV/NPV problems, always convert to a concrete population (like 1000 people) using the given prevalence. This makes the 2×2 table calculations much clearer than working with formulas alone.

Question 17

A screening test has sensitivity 88% and specificity 92%. If 1000 people are tested in a population where disease prevalence is 6%, how many false positives will occur?

  1. 72
  2. 75 (correct answer)
  3. 80
  4. 88
  5. 92
Explanation: When you encounter screening test questions, you're working with a 2×2 contingency table that breaks down test results by true disease status. The key is systematically calculating each cell using the given sensitivity, specificity, and prevalence. Start with your population of 1000 people. With 6% prevalence, you have 60 people with disease and 940 without disease. Sensitivity tells you about true positives: 88% of the 60 diseased people test positive, giving you 53 true positives (and 7 false negatives). Specificity tells you about true negatives: 92% of the 940 healthy people test negative, giving you 865 true negatives. The remaining healthy people who test positive are your false positives: 940−865=75940 - 865 = 75 false positives. Choice (B) 75 correctly applies this systematic approach. Choice (A) 72 likely results from a calculation error, possibly rounding 940 × 0.08 incorrectly. Choice (C) 80 might come from using 8% instead of the correct 8% false positive rate (100% - 92% specificity), or from other computational mistakes. Choice (D) 88 appears to confuse the sensitivity percentage with the actual count of false positives. For screening test problems, always construct the complete 2×2 table methodically: start with total population, apply prevalence to get diseased/healthy counts, then use sensitivity and specificity to fill in all four cells. False positives specifically come from the healthy population multiplied by (1 - specificity). This systematic approach prevents the mixing up of percentages and counts that creates most wrong answers.

Question 18

A test has sensitivity 75% and PPV 40% in a population with 8% disease prevalence. What is the test's specificity?

  1. 86.7%
  2. 89.1%
  3. 91.3% (correct answer)
  4. 93.5%
  5. 95.2%
Explanation: When you encounter diagnostic test questions involving sensitivity, specificity, and predictive values, you need to work systematically through the 2×2 table relationships. These problems test your understanding of how test characteristics interact with disease prevalence. Given the sensitivity (75%), PPV (40%), and prevalence (8%), you can calculate specificity by working through the diagnostic table. Start by assuming 1000 people in the population. With 8% prevalence, 80 people have disease and 920 don't. Since sensitivity is 75%, the test correctly identifies 75% of the 80 diseased people: 0.75×80=600.75 × 80 = 60 true positives. The remaining 20 diseased people are false negatives. Here's the key insight: PPV tells you that of all positive tests, 40% represent true disease. Since you have 60 true positives and PPV is 40%, you can find total positives: 60÷0.40=15060 ÷ 0.40 = 150 total positive tests. This means 150−60=90150 - 60 = 90 false positives. Finally, specificity is the percentage of healthy people correctly identified as negative: 920−90920=830920=0.913=91.3%\frac{920 - 90}{920} = \frac{830}{920} = 0.913 = 91.3\% Answer choice A (86.7%) likely comes from calculation errors in the table setup. Answer B (89.1%) and D (93.5%) represent common computational mistakes when working through the PPV relationship or confusing the sensitivity/specificity formulas. Remember: always set up the complete 2×2 table systematically. Use the given information to fill in what you know, then work step-by-step to find the missing values. PPV problems often require working backward from predictive values to find the test characteristics.

Question 19

A diagnostic test has a sensitivity of 85% and specificity of 90%. In a population where the disease prevalence is 2%, what is the positive predictive value (PPV)?

  1. 14.5% (correct answer)
  2. 17.0%
  3. 85.0%
  4. 90.0%
  5. 98.3%
Explanation: When you encounter diagnostic test questions involving sensitivity, specificity, and predictive values, you need to construct a 2×2 table and work through the calculations systematically. These questions test your understanding of how disease prevalence affects the interpretation of test results. To find the positive predictive value (PPV), start by assuming a population of 10,000 people. With 2% prevalence, 200 people have the disease and 9,800 don't. Given 85% sensitivity, the test correctly identifies 200×0.85=170200 \times 0.85 = 170 true positives and misses 30 cases. With 90% specificity, the test correctly identifies 9,800×0.90=8,8209,800 \times 0.90 = 8,820 true negatives, but incorrectly labels 9,800×0.10=9809,800 \times 0.10 = 980 as false positives. The total positive tests are 170+980=1,150170 + 980 = 1,150. PPV equals true positives divided by total positives: 1701,150=0.148\frac{170}{1,150} = 0.148 or 14.8%, making (A) 14.5% correct. (B) 17.0% might result from calculation errors in the 2×2 table setup. (C) 85.0% confuses PPV with sensitivity—a common mistake since both relate to positive results, but sensitivity asks "what percentage of diseased people test positive?" while PPV asks "what percentage of positive tests are truly diseased?" (D) 90.0% confuses PPV with specificity. Key takeaway: In low-prevalence populations, even highly accurate tests have surprisingly low positive predictive values due to the large number of false positives. Always construct the 2×2 table with actual numbers rather than working with percentages alone.

Question 20

A screening test correctly identifies 180 out of 200 patients with disease and correctly identifies 760 out of 800 patients without disease. What is the negative predictive value (NPV)?

  1. 90.0%
  2. 95.0%
  3. 97.4% (correct answer)
  4. 98.7%
  5. 99.0%
Explanation: When you encounter screening test questions, you're dealing with diagnostic test performance metrics. The key is organizing the data into a 2×2 table and understanding what each metric actually measures. First, let's construct the table from the given information:
  • True positives (TP): 180 (diseased patients correctly identified)
  • False negatives (FN): 20 (diseased patients missed: 200-180)
  • True negatives (TN): 760 (non-diseased patients correctly identified)
  • False positives (FP): 40 (non-diseased patients incorrectly identified: 800-760)
Negative predictive value (NPV) answers the question: "If a patient tests negative, what's the probability they truly don't have the disease?" The formula is: NPV=TNTN+FNNPV = \frac{TN}{TN + FN} Calculating: NPV=760760+20=760780=0.974=97.4%NPV = \frac{760}{760 + 20} = \frac{760}{780} = 0.974 = 97.4\% Answer A (90.0%) represents the sensitivity: 180200=90%\frac{180}{200} = 90\%, which measures how well the test identifies diseased patients. Answer B (95.0%) is the specificity: 760800=95%\frac{760}{800} = 95\%, measuring how well the test identifies non-diseased patients. Answer D (98.7%) appears to be a distractor with no corresponding calculation. Remember this pattern: NPV and PPV (positive predictive value) both have the same denominator structure—they include all patients with that particular test result. NPV includes all negative test results (TN + FN), while PPV includes all positive results (TP + FP). Always set up your 2×2 table first to avoid mixing up these metrics.