Calculate fictional STI test positivity and distinguish evidence from causal claims
Invented tested groups: A 30/500 = 6%; B 12/400 = 3%. Difference: 3 percentage points, or 50% lower relative to A. Positivity does not automatically mean community prevalence or a causal effect.
Section B15.5 · Sexually transmitted infections
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Recall pathogens, transmission routes, immune defence, viruses, blood and the difference between prevention and treatment.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is group B positivity for 12 positives among 400 tested?
What you will learn
- Use the number tested as the positivity denominator
- Distinguish percentage points relative change and population inference
Original teaching model. Invented data.
| Feature | Meaning |
|---|---|
| Group A | 30 positives / 500 tested = 6% |
| Group B | 12 positives / 400 tested = 3% |
| Absolute difference | 3 percentage points |
| Relative comparison | 50% lower relative to A |
Use the number tested as the positivity denominator
Two invented testing groups provide original arithmetic practice, not real surveillance or personal risk estimates. Group A has 30 confirmed positive results among 500 people tested; group B has 12 among 400 tested. Test positivity is positive results divided by the number tested, multiplied by 100. The denominator is the tested group, not an unspecified whole community or the positive count itself.
Group A positivity is 30 ÷ 500 × 100 = 6%, and group B positivity is 12 ÷ 400 × 100 = 3%. The absolute difference is 6 − 3 = 3 percentage points. Relative to group A’s positivity, group B is (6 − 3) ÷ 6 × 100 = 50% lower. These statements compare percentages using clearly identified denominators; 3 percentage points is not the same quantity as 3% relative reduction.
Distinguish percentage points relative change and population inference
Raw positive counts alone are not a fair comparison of positivity because the numbers tested differ. Neither tested-group percentage automatically gives whole-population prevalence: participation, selection, test timing and detection can affect which results appear. A testing record also cannot establish that an individual with a particular symptom or appearance has an infection.
The record does not assign groups randomly to a control measure or hold every relevant factor constant. A lower observed positivity therefore cannot prove that one particular campaign caused the difference. To evaluate a prevention claim, check selection, comparable testing methods, timing and other exposures. The original bars show the two observed tested-group proportions; they are not clinical probabilities or measured causal effects.
Sources for this lesson
Pause and explain
How should the difference between 6% and 3% be stated?
Worked example
Calculate positivity for 30 confirmed positives among 500 tested.
Show the worked solution
- Divide 30 by the tested denominator 500.
- Multiply by 100 and label the result.
Answer 30 ÷ 500 × 100 = 6% test positivity.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Calculate positivity for both invented groups: A 30 of 500 tested, B 12 of 400 tested.
Give me a hint
Use a separate tested denominator for each group.
Compare my reasoning
- Calculate 30 ÷ 500 × 100.
- Calculate 12 ÷ 400 × 100.
A has 6% test positivity; B has 3% test positivity.
Look for these in your work
- Use both tested denominators
- Label positivity
Calculate the absolute percentage-point difference and relative reduction from A 6% to B 3%.
Give me a hint
Use subtraction first, then the starting 6% denominator.
Compare my reasoning
- Subtract 3 from 6 for the absolute difference.
- Divide 3 by 6 and multiply by 100 for relative reduction.
The difference is 3 percentage points; B is 50% lower relative to A.
Look for these in your work
- Distinguish percentage points
- Use the correct relative baseline
A fictional report calls B’s 3% whole-community prevalence and proof that a campaign caused the difference. Evaluate both claims.
Give me a hint
Check who was tested and whether a cause was isolated.
Compare my reasoning
- Separate tested-group positivity from population prevalence.
- Check selection and other uncontrolled factors.
Neither claim follows: 3% describes the tested group, and differences in selection, timing or other factors prevent this record alone from proving a campaign caused the difference.
Look for these in your work
- Retain the sample scope
- Reject unsupported causation
Common mistakes
- Use the number tested, not only the positive count.
- Test positivity is not automatically population prevalence or causal effect.
What can you explain now?
How should the difference between 6% and 3% be stated?
Compare with the explanation
3 percentage points; 50% lower relative to 6%
Absolute and relative differences use different calculations.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Explain use the number tested as the positivity denominator and distinguish percentage points relative change and population inference. Use the stated route, conditions and evidence before opening the solutions.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.