Research navigation: Expand a section index to jump to a worked exercise, interpretation or research design check.
Study Designs and Basic Comparisons
- A University Research Question Must Be Answerable
- The Design Choices: Cohort, Case-Control and Cross-Sectional
- Worked Research Exercise 1. Define an estimand
- Worked Research Exercise 2. Distinguish observation and inference
- Worked Research Exercise 3. Report the right region
- Worked Research Exercise 4. Spot an ecological fallacy
- Worked Research Exercise 5. Identify a confounder
- Worked Research Exercise 6. Identify a mediator
- Worked Research Exercise 7. Identify effect modification
- Worked Research Exercise 8. Risk in a Group
- Worked Research Exercise 9. Comparison Risk
- Worked Research Exercise 10. Relative Risk
Risk, Odds and Estimation
- Worked Research Exercise 11. Risk Difference
- Worked Research Exercise 12. Odds in a Group
- Worked Research Exercise 13. Odds Ratio
- Worked Research Exercise 14. Confidence Interval Width
- Worked Research Exercise 15. Standard Error
- Worked Research Exercise 16. A Mean’s 95% Interval
- Worked Research Exercise 17. Cross-Sectional Limitation
Bias, Confounding and Causal Contrasts
- Worked Research Exercise 18. Follow-Up Attrition
- Worked Research Exercise 19. Missing Data
- Worked Research Exercise 20. Exposure Error
- Worked Research Exercise 21. Selection Bias
- Worked Research Exercise 22. Recall Bias
- Worked Research Exercise 23. Ecological vs Individual
- Worked Research Exercise 24. Difference-in-Differences
- Worked Research Exercise 25. Parallel Trends
- Worked Research Exercise 26. Correlation
- Worked Research Exercise 27. Multiple Testing
- Worked Research Exercise 28. Sensitivity Analysis
- Worked Research Exercise 29. Information Ethics
- Worked Research Exercise 30. Write a Careful Conclusion
Reporting, Ethics and Continue Reading
The Direct Answer: Association Is Not Causation
How can university students study Singapore haze without making unsupported health or environmental claims? Define the research question, identify exposure and outcome precisely, examine a plausible causal pathway, consider confounders and selection bias, choose a suitable design, estimate uncertainty and report what the data can actually establish. Correlation alone does not prove cause, even when two time-series curves move in the same direction.
This university-level guide gives 30 original research-design exercises, worked numerical examples and practical explanations of sampling, relative risk, odds ratios, ecological fallacy, difference-in-differences and responsible interpretation. It draws on STROBE, the international reporting guideline for observational studies, and the US EPA’s guidance on planning air-sensor studies. These sources guide rigorous reporting and sensor use; they do not validate any particular fictional example here.
Punggol makes the issue locally understandable because families, schools and workers respond to haze differently. NEA publishes outdoor readings for North, which contains Punggol; that regional reading does not measure an individual’s medical history or indoor exposure. Actual health advice belongs to NEA’s live haze service and the relevant healthcare professionals.
A University Research Question Must Be Answerable
A weak question says: “Does haze harm everyone?” It is too broad, with no defined outcome, population, time or method. A stronger observational question could be: “In a suitably designed dataset, are measured hourly PM2.5 concentrations associated with a clearly defined outcome after accounting for specified weather and calendar factors?”
This improved question still does not guarantee a causal answer. The variables and data structure determine what can be investigated responsibly. An outcome based on anonymous aggregate counts differs from individual clinical outcomes with stringent privacy requirements.
A student should also identify the target population. One convenience sample taken near a Punggol library cannot be assumed to describe all Singapore residents, much less everyone in Southeast Asia.
The first successful research product is a precise question, a defined data dictionary and an explicit list of major alternative explanations.
The Design Choices: Cohort, Case-Control and Cross-Sectional
The STROBE statement covers reporting for cohort, case-control and cross-sectional observational studies. A cohort follows or analyses groups over time; a case-control design compares people selected by outcome status; a cross-sectional design examines a defined population or sample at one period.
These are different designs with different strengths and limitations. Their measures and sampling procedures cannot be treated as interchangeable just because all produce percentages.
A cross-sectional survey of activity preferences can describe responses but may not establish whether a health condition preceded an exposure. A case-control design requires care about how cases and controls were selected. A cohort depends on follow-up quality and comparability.
STROBE is a reporting guideline, not a guarantee that a study is unbiased or a checklist that magically proves causation.
An Orientation Table for Different Research Readiness
A student should begin with the earliest unstable inference skill before writing an ambitious causal thesis.
| Current research skill | Appropriate first task | A defensible next step |
|---|---|---|
| Introductory data literacy | Define units, times and categories | Explore distributions and missingness |
| Basic statistics | Fractions, risks and sampling | Confidence intervals and study design |
| Comfortable with regression | Identify alternative explanations | Model confounders explicitly |
| Familiar with causal diagrams | Draw plausible pathways | Compare estimands and assumptions |
| Capstone or thesis | Specify protocol and governance | Sensitivity analysis and clear reporting |
This is a teaching orientation, not a formal syllabus or study-placement requirement for SIT or another university. The institution and research supervisor determine the relevant coursework and ethics process.
Exposure: What Does North-Region PM2.5 Actually Represent?
NEA reports regional one-hour PM2.5 concentrations in µg/m³ and the 24-hour PSI index under different methods. The region containing Punggol is North, a much broader area than a single address.
Assigning the same regional reading to everyone in a dataset is a coarse exposure proxy. People may spend different amounts of time indoors, travel to other regions, work outside or use varying ventilation and filtration.
A research paper must explain whether it measures ambient regional pollution, a personal sensor reading, a modelled local concentration or an actual individual exposure estimate. Those are not identical variables.
Conflating them can produce exposure misclassification. Before fitting regression, examine how exposure was measured and which limitations cannot be repaired by adding more decimal places.
A Causal Diagram in Words
Imagine a hypothetical diagram with regional smoke → measured outdoor PM2.5 → individual exposure → a specified outcome. Additional variables may influence several parts of this pathway: weather affects smoke transport and outdoor activity; an individual’s work and building conditions affect personal exposure; health status affects vulnerability and behaviour.
This is an illustrative causal graph, not a complete medical or atmospheric model. A causal diagram should be based on domain knowledge and proposed assumptions rather than built by connecting every variable that happens to correlate in a spreadsheet.
A confounder influences both the exposure and outcome in a way that can distort the association. A mediator lies along a pathway from exposure to outcome. An effect modifier changes how the relationship differs across groups.
The distinction matters because adjusting for every available variable indiscriminately can introduce bias rather than remove it.
Why the Counterfactual Matters
Causal inference asks what would have happened to the same target unit or population under a different exposure or intervention condition. In reality, a person cannot simultaneously live through exactly the same hour with and without one particular exposure.
Research designs use comparisons, assumptions and sometimes natural experiments to approximate that missing counterfactual. Better data help, but more measurements do not by themselves eliminate unmeasured differences.
This is why a before-and-after chart is not automatically the effect of a policy. Weather, season, source fire activity or broader events may change at the same time.
A careful research claim states the assumed comparison and tests whether alternative explanations could account for the observed difference.
Source Attribution and Legal Responsibility Are Separate
Satellite fire hotspots, regional wind analyses and ground PM2.5 readings can support scientific investigation of smoke transport. But a hotspot alone does not establish who ignited a fire, what fuel burned, or whether a particular company has violated a law.
Environmental source attribution and legal liability are different processes with distinct evidence standards. A university report should be explicit about whether it is analysing statistical association, potential smoke transport or a legal finding.
For the regional legal framework, see Punggol Haze and ASEAN Regional Law. For reading hotspots and wind data, see Punggol Haze Data Literacy.
A responsible student never turns a hypothetical model coefficient into an allegation about an identifiable party.
All Worked Results Below Are Fictional
Every numerical table and research result below is a fabricated educational example. The purpose is to demonstrate how a research estimate is calculated and interpreted under specified assumptions.
No quoted fraction represents actual illness among Punggol residents. No difference-in-differences figure estimates the effect of a real policy. No relative risk shown below is an epidemiological result about actual transboundary haze.
Whenever a fictional model describes potential health outcomes, it uses neutral simulated categories and explicitly avoids clinical recommendations. Students should not collect identifiable health details or conduct unauthorised experiments.
The original data source, population and method always matter more than the number of decimal places in the output.
Worked Research Exercise 1. Define an estimand
Research question. A research proposal says ‘haze affects society’. What is missing?
Correct calculation or answer. Specify the population, exposure/intervention, outcome, comparison and time frame.
What it actually supports. Without a target estimand, a regression coefficient may not answer the intended question.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 2. Distinguish observation and inference
Research question. A Punggol photo shows a pale skyline. Does it prove PM2.5 was 180 µg/m³?
Correct calculation or answer. No. The photo observes appearance, while concentration requires the relevant measurement.
What it actually supports. Humidity, distance and camera processing can affect visibility.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 3. Report the right region
Research question. A data analyst writes ‘Punggol block 123 PSI’ using an NEA North-region reading.
Correct calculation or answer. Relabel it North-region PSI with its timestamp and source.
What it actually supports. A regional statistic does not justify block-level precision.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 4. Spot an ecological fallacy
Research question. A North-region average is elevated and a resident reports coughing. Does that prove the resident inhaled the regional average?
Correct calculation or answer. No. Group data cannot determine one individual’s exposure or cause of symptoms.
What it actually supports. Personal location, building conditions and other factors are missing.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 5. Identify a confounder
Research question. A fictional study compares outdoor sport and reported discomfort; hot weather influences both.
Correct calculation or answer. Temperature or heat is a plausible variable to examine as a confounder.
What it actually supports. Confounding depends on the proposed causal structure, not a variable’s correlation alone.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 6. Identify a mediator
Research question. In a hypothetical causal model, smoke affects indoor particles through open windows.
Correct calculation or answer. Indoor concentration may be a mediator on a pathway from outdoor smoke to personal exposure.
What it actually supports. Adjusting for mediators changes the causal question being estimated.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 7. Identify effect modification
Research question. A fictional effect estimate differs across categories of outdoor activity duration.
Correct calculation or answer. Duration may act as an effect modifier if the relationship truly varies by subgroup.
What it actually supports. An interaction claim requires appropriate evidence and sufficient data.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 8. Risk in a Group
Research question. Twenty of 100 invented exposed participants experience a binary simulated outcome.
Correct calculation or answer. Risk =20/100 = 20%.
What it actually supports. This is a purely hypothetical proportion, not measured real health outcomes.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 9. Comparison Risk
Research question. Ten of 100 invented comparison participants have the simulated outcome.
Correct calculation or answer. Risk =10/100 = 10%.
What it actually supports. The two groups’ comparability and selection must be assessed before causal interpretation.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 10. Relative Risk
Research question. Use the hypothetical risks 20% and 10%.
Correct calculation or answer. RR=0.20/0.10= 2.0.
What it actually supports. Twice the risk in fictional groups is an association measure, not proof the exposure caused the difference.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 11. Risk Difference
Research question. Use the same hypothetical groups.
Correct calculation or answer. RD=0.20−0.10 = 0.10, or 10 percentage points.
What it actually supports. Absolute and relative contrasts communicate different aspects of a comparison.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 12. Odds in a Group
Research question. Twenty simulated outcomes and eighty non-outcomes among one hundred.
Correct calculation or answer. Odds =20/80 = 0.25.
What it actually supports. Odds are not the same as probability; probability here is 0.20.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 13. Odds Ratio
Research question. Exposed: 20 cases,80 noncases; comparison:10 cases,90 noncases.
Correct calculation or answer. OR=(20×90)/(80×10) = 2.25.
What it actually supports. OR differs from the RR of 2.0 in this example, especially important when interpreting case-control studies.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 14. Confidence Interval Width
Research question. A fictional estimate is 4.0 with CI [2.5,5.5]. Find the width.
Correct calculation or answer. 5.5−2.5 = 3.0 units.
What it actually supports. Report the estimate and CI with the target parameter; width alone does not establish bias-free design.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 15. Standard Error
Research question. Assume independent random observations with known σ=12 and n=36.
Correct calculation or answer. SE=12/√36 = 2.
What it actually supports. Closely spaced hourly values may be correlated and invalidate the simple independent-observation assumption.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 16. A Mean’s 95% Interval
Research question. Assume sample mean60, known σ12, n36 with valid independent sampling.
Correct calculation or answer. 60±1.96(2) = [56.08,63.92].
What it actually supports. This confidence interval targets a population mean under assumptions, not tomorrow’s individual pollution reading.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 17. Cross-Sectional Limitation
Research question. A survey collects exposure and reported symptoms on the same day. Does it show which came first?
Correct calculation or answer. Not necessarily; temporal ordering may be uncertain.
What it actually supports. Cross-sectional evidence often limits causal conclusions.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 18. Follow-Up Attrition
Research question. A hypothetical cohort begins with 200 people and 170 complete follow-up.
Correct calculation or answer. Retention=170/200×100 = 85%; attrition 15%.
What it actually supports. Loss to follow-up may introduce bias if related to outcome or exposure.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 19. Missing Data
Research question. Seven of twenty-eight scheduled fictional sensor records are missing.
Correct calculation or answer. Missingness=7/28 = 25%.
What it actually supports. Do not replace missing readings with zero without an appropriate reason.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 20. Exposure Error
Research question. A fictional instrument reads 66 compared with a matched reference 60.
Correct calculation or answer. Signed difference +6, relative difference 10%.
What it actually supports. A single paired measurement is not a complete sensor validation study.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 21. Selection Bias
Research question. A survey about outdoor exercise recruits only people already at a park.
Correct calculation or answer. The sampling frame may overrepresent outdoor users.
What it actually supports. A large sample from one narrow frame can remain unrepresentative.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 22. Recall Bias
Research question. Participants are asked to remember precise smoke exposure from many months ago.
Correct calculation or answer. Recall may be imperfect and systematically different across respondents.
What it actually supports. Consider dated measurements and appropriate exposure reconstruction.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 23. Ecological vs Individual
Research question. A regional graph is correlated with an aggregate count. Can one infer the exposure of a named household?
Correct calculation or answer. No. Aggregate associations do not identify individual values.
What it actually supports. Maintain the study’s unit of analysis when explaining conclusions.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 24. Difference-in-Differences
Research question. A fictional intervention group changes from 30 to 25; control from 40 to 43.
Correct calculation or answer. DID=(25−30)−(43−40)=−5−3= −8 units.
What it actually supports. A causal DID interpretation needs assumptions, notably an appropriate counterfactual trend.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 25. Parallel Trends
Research question. Only one before and after point is supplied for the DID example. Is parallel trends established?
Correct calculation or answer. No. A historical pre-intervention series and contextual evidence would be needed.
What it actually supports. The equation gives a contrast, not an automatically unbiased policy effect.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 26. Correlation
Research question. A fictional analysis finds Pearson r=0.8.
Correct calculation or answer. It describes a strong positive linear association in the studied sample.
What it actually supports. It does not establish direction of causality or rule out confounding.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 27. Multiple Testing
Research question. Suppose twenty independent null tests each use α=0.05. What is the expected number of false rejections?
Correct calculation or answer. 20×0.05 = 1 expected false rejection.
What it actually supports. This is an expectation under stated assumptions, not a guarantee that exactly one result will be false.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 28. Sensitivity Analysis
Research question. A conclusion changes substantially when one questionable outlier is retained versus excluded.
Correct calculation or answer. Report both analyses and the prespecified handling rule.
What it actually supports. Suppressing the inconvenient result would misrepresent uncertainty.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 29. Information Ethics
Research question. A proposed dataset includes named children, addresses and private medical notes. May it be published to improve transparency?
Correct calculation or answer. No, not without appropriate lawful authority, consent and privacy safeguards.
What it actually supports. Reproducibility can use synthetic or properly de-identified fixtures rather than disclosing private records.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
Worked Research Exercise 30. Write a Careful Conclusion
Research question. A fictional study reports an association but cannot exclude weather-related confounding.
Correct calculation or answer. Say ‘associated with’ and explain the limits, not ‘proved to cause’.
What it actually supports. The strength of the language should not exceed the strength of the evidence.
Clementi-style error diagnosis. Identify whether a mistake arises from choosing the wrong denominator, confusing odds with risk, ignoring the sampling design, using the wrong level of aggregation or claiming more causality than the comparison supports. Rerun the method on a changed fictional dataset to establish independent mastery.
Reporting boundary. Every figure here is simulated. The result must not be presented as an observed health association, national air-quality condition, legal finding or recommendation for a real person.
How to Interpret Risk and Odds Without Confusing Them
A risk is the proportion of a defined group with a specified binary outcome over a defined period. Odds compare that proportion with the proportion without the outcome. They are related but not numerically identical.
In the fictional exposed group, twenty out of one hundred gives risk 0.20 and odds 20/80=0.25. In the comparison group, the risk is 0.10 and odds 10/90≈0.1111. The relative risk is 2.0, while the odds ratio is 2.25.
A student who swaps an OR for an RR in a public communication may overstate the interpretation. The sampling scheme and outcome prevalence affect whether the distinction is important.
Even a perfectly computed RR or OR can reflect confounding, bias or chance. Correct arithmetic is necessary, but not sufficient, for causal inference.
Why Difference-in-Differences Needs Parallel Trends
The fictional DID contrast of −8 units compares the intervention group’s change with the comparison group’s change. The arithmetic subtracts off the observed control-group trend.
However, attributing that difference to an intervention generally depends on whether the groups would have followed sufficiently comparable trends without it, along with other design considerations. A single pre- and post-observation cannot establish that assumption.
For a haze-related intervention, the groups might experience different rain, transport patterns or building conditions. These could change outcomes independently of the intervention.
A good dissertation would use appropriate prior trends, contextual evidence, robustness checks and cautious interpretation rather than announcing an eight-unit causal improvement from one small table.
Ecological Fallacy and Exposure Misclassification
NEA’s North-region outdoor monitoring is useful for public information, but the reported region covers a broad geography. A resident’s actual exposure depends on where they live and work, activity duration, ventilation, filtration and other circumstances.
A researcher assigning the same ambient regional concentration to every person may make a necessary simplifying assumption in some designs. But they must describe it as an approximation, assess likely misclassification and avoid pretending the dataset contains room-level measurements.
Likewise, an observed association between regional pollution and aggregate counts cannot independently diagnose a named resident. Moving from group averages to claims about individuals is the ecological fallacy.
The statistical analysis should remain at the level of evidence actually available.
Sampling, Missingness and Selection Bias
A sample collected only from people in a library will tend to include people willing or able to use that venue. It does not automatically represent everyone outdoors, everyone working from home or all Punggol residents.
Missing information creates further problems. A respondent’s absence may be related to health, work pattern or willingness to disclose personal data. A sensor may fail under specific meteorological conditions.
A complete-case analysis should therefore discuss whether missingness or selection could systematically change the estimate. An increase in sample size does not repair a selection process that repeatedly excludes the same groups.
Describe who could enter the dataset, who actually did, who dropped out and what the analytical population represents.
A Cross-Sectional Finding Cannot Reconstruct Time Automatically
A cross-sectional dataset captures exposure and outcome measures within a period. It is often helpful for describing prevalence and patterns, but the timing may not reveal whether exposure came before an outcome.
A retrospective report can suffer recall bias, while a prospective cohort can lose participants during follow-up. Each design offers some advantages and trade-offs.
The choice should follow the precise question rather than the technique the student most recently learnt in a statistics module. No observational design becomes causal solely because regression software produces small p-values.
STROBE provides structured prompts for transparent reporting of such designs, but its checklist is not a substitute for designing a valid study.
Sensitivity Analysis Is a Core Part of Honest Research
A sensible study examines whether results change when plausible analytical choices change—for example, retaining versus investigating an outlier, selecting a different valid adjustment set, or using a different measurement proxy.
A robust result may remain directionally similar across justifiable specifications; a fragile one may disappear. Neither response should be hidden. The purpose of sensitivity analysis is to show how much the conclusion depends on assumptions.
A university report should distinguish prespecified plans from exploratory analyses. Quietly trying many versions and reporting only the most dramatic can create misleading evidence.
Transparent negative and uncertain findings are useful outcomes, particularly when public policy or health interpretation might be affected.
Four-Week University Research Methods Plan
Week 1 — Define: Formulate an answerable question, the target population, exposure, outcome, comparison, unit and period. Write a data dictionary.
Week 2 — Designs and bias: Compare cohort, case-control and cross-sectional designs. Draw a basic causal diagram and identify plausible confounders, mediators and selection factors.
Week 3 — Quantify carefully: Work through relative risk, odds ratio, absolute differences, missingness, uncertainty and a fictional difference-in-differences example.
Week 4 — Report: Write a two-page methods-and-limitations note including an alternative explanation, privacy review, sensitivity analysis and a conclusion no stronger than the evidence.
This is a self-study framework, not an official module for any particular autonomous university. Actual research with people requires the relevant institutional approvals.
Frequently Asked Questions
Can a high correlation coefficient prove haze caused an outcome?
No. Correlation may reflect confounding, chance, selection or other relationships.
Why do risk and odds ratios differ?
They use different denominators. Risk compares events with everyone in the group; odds compare events with non-events.
Is a regional PM2.5 number an individual’s exact exposure?
No. A regional outdoor measurement does not determine personal indoor conditions, location or activity.
Can difference-in-differences prove a policy succeeded from two points?
Not by itself. Appropriate parallel-trends and other design assumptions require investigation.
Does a small p-value prove the null is false?
It describes data compatibility with a specified statistical null under assumptions; it is not a direct probability that the null is true or false.
What does the STROBE guideline cover?
Reporting of observational cohort, case-control and cross-sectional studies. It is not a certification of causal validity.
Should students publish medical records with a reproducible notebook?
No. Privacy and ethical governance must be respected. Synthetic or appropriately governed data can support verification.
Why is an outlier not automatically deleted?
It may be a real observation or an error. Exclusion requires a justified, reported rule and investigation.
What is ecological fallacy?
Assuming a group-level pattern necessarily applies to a particular individual.
Are the worked statistics actual Punggol health figures?
No. All numerical examples are fictional and are not a health advisory, diagnosis or study result.
Continue Through the University and Punggol Haze Library
For introductory statistics, use Polytechnic Applied Statistics and Punggol Haze. For data pipelines, use SIT Punggol Applied AI Haze Project Guide. For even earlier foundations, read ITE Higher Nitec Applied Numeracy.
The Punggol Haze Data Literacy article covers charts, hotspots and units, while Why Punggol Haze Changes Hour by Hour explains weather variation that researchers must consider.
The Punggol Haze Complete Guide is the wider reference hub. This article’s specific purpose is university research design and interpretation, especially the limits of observational causal claims.
Official Sources, Research Scope and Ethical Limits
Reviewed 20 October 2026. Every percentage, relative risk, odds ratio, confidence interval, sample count and intervention contrast in the worked exercises is made up for education. No source here establishes the hypothetical results in Punggol.
- EQUATOR Network: STROBE Guidelines for Observational Studies
- US EPA: Enhanced Air Sensor Guidebook
- NEA: Air-Pollution FAQs, PSI, PM2.5 and Reporting Regions
- data.gov.sg: NEA Real-Time PM2.5 Data Documentation
- NEA: Live Haze Health Guidance
The best research paper makes the reader understand the question, comparison, calculations, plausible biases, uncertainty and exactly what remains unproven. Scientific confidence grows from respecting those boundaries.
