eduKateSG · Why Science?
Name the statistical question, assumptions and output—not only the test label or final p-value
Choose the stage of analysis you need to inspect, then follow the evidence chain from design and variables to assumptions, results and interpretation.
Science learning becomes powerful when a statistical result can be traced back to the question, design, variables, assumptions and observations that produced it. The OBO Foundry describes STATO as a general-purpose statistics ontology covering statistical tests, their conditions of application, probability distributions, variables, spread and variation metrics, experimental design, plots and graphical representations. The official page notes documented applications including factorial design, association studies, differential expression, hit selection and meta-analysis, and says STATO interoperates with Basic Formal Ontology and the Ontology for Biomedical Investigations. STATO can describe an analysis consistently, but correct vocabulary does not guarantee suitable sampling, satisfied assumptions or a justified conclusion. This guide supports Primary Science, PSLE Science, Secondary Science, O-Level Science, mathematics, computing and STEM education as a longform evidence-reading route; it is not statistical, medical, admission or career advice.
Related eduKate reading: Information Artifact Ontology; Ontology for Biomedical Investigations; Evidence and Conclusion Ontology; UCUM and unambiguous measurement units; Science Learning Hub; Education Hub; STEM Education; Careers by Subject Capability.
Primary and official sources checked on 13 October 2026: OBO Foundry Statistical Methods Ontology overview, checked 13 October 2026; Official STATO project website; Official STATO source repository; Canonical STATO OWL release; 2026 Singapore–Cambridge O-Level Biology syllabus; MOE G2/G3 Lower Secondary Science teaching and learning syllabus; 2026 MOE G2 Computing syllabus. Ontologies, definitions and release products can change, so preserve dated documentation, exact source records and file versions.
How a statistical method becomes an auditable scientific argument
A test name is not a complete analysis. The same test can answer different questions depending on the outcome, predictor, sampling unit, grouping, model formula and alternative hypothesis.
The OBO Foundry says STATO covers statistical tests and their conditions of application. This matters because a method label without its assumptions can make a result look more portable than it is.
STATO also covers probability distributions, variables, spread and variation metrics. These are connected pieces: a variable has a measurement scale, a model invokes a distribution and an output summarises uncertainty under stated conditions.
Experimental design is part of the official scope. Randomisation, blocking, pairing, repeated measures and factorial structure shape which comparisons are valid before software calculates anything.
Plots are not decorative extras. The official scope includes graphical representations used to show data distribution or layout and assist review of results. A plot can reveal skew, clusters, outliers or heterogeneity hidden by one summary number.
The page documents applications beyond one field, including association studies, differential expression and meta-analysis. A shared ontology can make method records comparable while each domain retains its scientific context.
STATO relies on BFO and OBI for interoperability. A frozen analysis therefore includes the STATO release and relevant imported ontology versions, not just a local label such as “t-test”.
A p-value is an output under a model and hypothetical repetition logic; it is not the probability that the hypothesis is true. Ontology can type the value, while explanation must protect its interpretation.
Effect size and uncertainty usually answer more useful questions than significance alone. A small effect can be precisely estimated, and a large estimate can remain too uncertain for a firm conclusion.
Independence depends on study structure. Many cells from one specimen or repeated readings from one participant are not automatically independent replicates.
Software defaults are methodological choices. Reference levels, missing-value rules, variance estimators, optimisation settings and multiple-testing corrections belong in the provenance record.
The optimistic purpose is inspectability: researchers can compare analysis plans, locate assumption failures and rerun results without treating a statistical label as a magic spell.
Begin with the estimand—the quantity the study aims to learn about. A model can be calculated perfectly while targeting a different population, contrast or time point from the scientific question.
Define the observational and experimental units. Confusing specimens, technical replicates and biological replicates inflates apparent sample size and narrows uncertainty unjustifiably.
Keep variable roles separate: outcome, predictor, covariate, blocking factor, weight and identifier are not interchangeable columns.
Measurement scale constrains reasonable operations. Counts, proportions, continuous measurements, ordered categories and nominal labels invite different models and diagnostics.
Missingness has mechanisms and consequences. Complete-case analysis, imputation and model-based handling each require assumptions that must be documented.
Model diagnostics should be linked to the fitted model and dataset version. A residual plot saved without those references cannot audit the analysis it supposedly checks.
Multiple testing changes interpretation because many opportunities for chance extremes were examined. Record the family of tests, correction method and both raw and adjusted outputs.
A confidence interval communicates a range produced by a procedure under assumptions; it is not a guarantee that every plausible mechanism lies inside.
For classroom investigations, students can compare a table, a graph, a mean and the individual observations, noticing what each representation keeps or compresses.
Reader-ready reporting names the question, sample, design, method, assumptions, effect estimate, uncertainty, software and limitations before offering a conclusion.
Pre-specification protects against silently choosing methods after seeing which result looks most exciting. Amendments can be valid, but they need dates, reasons and a distinction from the original plan.
Outlier handling is not a cleanup reflex. Investigate data errors, measurement limits and genuine rare cases, then report rules and sensitivity analyses.
Transformations alter the scale on which effects are modelled. Back-transformed summaries may be useful, but the fitted scale and assumptions remain part of the method.
Meta-analysis combines estimates under explicit models of within-study and between-study uncertainty. Similar topic labels do not guarantee compatible populations, outcomes or designs.
A statistically significant association can remain confounded, biased or too small to matter practically. Causal interpretation needs design and assumptions beyond the p-value.
Versioned code is part of statistical evidence. Package updates can change defaults, algorithms or numerical behaviour even when the written method name stays constant.
Random seeds help reproduce stochastic computation, but exact reruns also need data, code, environment, dependency versions and hardware-relevant details where necessary.
Ontology mappings should distinguish exact statistical equivalence from broad relatedness. Two procedures may share a family label while estimating different targets or using different variance assumptions.
Before combining results, build an analysis inventory listing population, design, unit, variables, model, contrast, missingness, software, outputs and diagnostics. It makes hidden differences discussable.
STATO supports the language of analysis; scientific judgement still evaluates whether the data, assumptions and interpretation make the conclusion worth believing.
A statistical workflow also needs decision provenance. Record who approved the analysis plan, which quality checks were automated, which warnings required human judgement and why any planned step was changed. This is especially important when one pipeline produces many results: a shared method label does not reveal where an analyst intervened or which branches ran only for selected variables.
Reproduction and replication answer different questions. Reproduction asks whether the reported computation can be rerun from the same data and methods; replication asks whether new observations support a compatible finding. A STATO-based record can clarify the analysis performed, while independent data collection and scientific comparison remain necessary for stronger confidence.
| Stage | Question | Evidence | Responsible output |
|---|---|---|---|
| Design | What question and sampling plan generated the data? | Population, unit, variables, assignment and protocol | A bounded estimand and study design |
| Check | Which assumptions and diagnostics apply? | Distribution, independence, missingness and model checks | A justified analysis route |
| Estimate | What method and output were produced? | STATO identifiers, software, parameters and uncertainty | A traceable result |
| Interpret | What does the result support—and not support? | Effect, interval, limitations and alternative explanations | A calibrated conclusion |
Inside this guide
1–12 · Question, design and variables
- 1. Begin with the scientific question
- 2. Define the estimand
- 3. Identify the study design
- 4. Identify the observational unit
- 5. Identify variable roles
- 6. Check measurement scales
- 7. Use the STATO identifier
- 8. Read conditions of application
- 9. Describe distributions
- 10. Describe variation
- 11. Describe graphical checks
- 12. Describe the comparison
13–24 · Methods, outputs and reproducibility
- 13. Handle missing data
- 14. Handle transformations
- 15. Handle multiple testing
- 16. Estimate effect size
- 17. Quantify uncertainty
- 18. Record software and parameters
- 19. Preserve random seeds
- 20. Link diagnostics
- 21. Separate planned and exploratory work
- 22. Audit data exclusions
- 23. Challenge p-value certainty
- 24. Challenge independence
25–36 · Learning, communication and pathways
- 25. Challenge causal language
- 26. Challenge model fit
- 27. Review ontology and code migration
- 28. Connect to Primary Science
- 29. Connect to Secondary Science
- 30. Connect to mathematics
- 31. Connect to computing
- 32. Connect to pathways
- 33. Did you know?
- 34. Write a reader-ready analysis note
- 35. Build a validation ladder
- 36. Finish with a reproducible analysis bundle
Section 1 of 36
1. Begin with the scientific question
Statistical work starts with what the study wants to learn, not with the menu of tests available in software.
Working checkpoint — STATO identifier: Write the population, outcome, comparison and time frame. Keep question, estimand, design, variables, model, software and outputs in one analysis record.
For mathematics, connect formulas to the design assumptions that make them meaningful.
Section 2 of 36
2. Define the estimand
The estimand states the quantity to be estimated, such as a mean difference, rate ratio or association under a defined population.
Working checkpoint — statistical variable: Make the target explicit before choosing a model. Link every assumption check and diagnostic to the exact data and fitted model.
For computing, preserve executable code, dependency versions and machine-readable method identifiers.
Section 3 of 36
3. Identify the study design
Randomised, observational, paired, repeated-measures and factorial designs create different dependence and bias structures.
Working checkpoint — study design: Name assignment, sampling, blocking and follow-up. Report effect size, uncertainty and limitations alongside any significance measure.
For writing, distinguish observation, estimate, uncertainty and interpretation in separate sentences.
Section 4 of 36
4. Identify the observational unit
The unit that contributes independent information may be a participant, specimen, site or time series—not every recorded row.
Working checkpoint — probability distribution: Draw the nesting structure before counting sample size. Separate planned, exploratory and sensitivity analyses instead of merging their narratives.
For students, ask what the graph shows that the average hides.
Section 5 of 36
5. Identify variable roles
Outcome, predictor, covariate, factor, identifier and weight guide how software interprets columns.
Working checkpoint — test statistic: Create a variable dictionary with role and scale. Pin ontology, code, package and data versions before attempting reproduction.
For parents, the useful checkpoint is whether the child can explain the conclusion in ordinary language.
Section 6 of 36
6. Check measurement scales
Continuous, count, binary, ordered and nominal variables support different summaries and models.
Working checkpoint — analysis provenance: Verify coding and allowed values against the protocol. Keep question, estimand, design, variables, model, software and outputs in one analysis record.
For mathematics, connect formulas to the design assumptions that make them meaningful.
Section 7 of 36
7. Use the STATO identifier
A STATO class gives the method or output a stable reference beyond local spelling.
Working checkpoint — STATO identifier: Store identifier, label, definition and release. Link every assumption check and diagnostic to the exact data and fitted model.
For computing, preserve executable code, dependency versions and machine-readable method identifiers.
Section 8 of 36
8. Read conditions of application
The official scope includes assumptions and conditions, not just test names.
Working checkpoint — statistical variable: List the required design and distribution conditions. Report effect size, uncertainty and limitations alongside any significance measure.
For writing, distinguish observation, estimate, uncertainty and interpretation in separate sentences.
Section 9 of 36
9. Describe distributions
Probability distributions model possible values under assumptions and connect parameters to observations.
Working checkpoint — study design: State the distribution and why it is plausible. Separate planned, exploratory and sensitivity analyses instead of merging their narratives.
For students, ask what the graph shows that the average hides.
Section 10 of 36
10. Describe variation
Range, variance, standard deviation and robust spread summaries answer different questions about dispersion.
Working checkpoint — probability distribution: Choose a measure that matches scale and distribution. Pin ontology, code, package and data versions before attempting reproduction.
For parents, the useful checkpoint is whether the child can explain the conclusion in ordinary language.
Section 11 of 36
11. Describe graphical checks
Plots can reveal skew, non-linearity, clustering and influential observations before a summary statistic does.
Working checkpoint — test statistic: Link every plot to its source data version. Keep question, estimand, design, variables, model, software and outputs in one analysis record.
For mathematics, connect formulas to the design assumptions that make them meaningful.
Section 12 of 36
12. Describe the comparison
A model may contain many coefficients; the scientific contrast identifies which combination answers the question.
Working checkpoint — analysis provenance: Write the contrast in words and code. Link every assumption check and diagnostic to the exact data and fitted model.
For computing, preserve executable code, dependency versions and machine-readable method identifiers.
Section 13 of 36
13. Handle missing data
Missing values can arise for different reasons, and the handling method can change the target population.
Working checkpoint — STATO identifier: Record missingness codes, patterns and assumptions. Report effect size, uncertainty and limitations alongside any significance measure.
For writing, distinguish observation, estimate, uncertainty and interpretation in separate sentences.
Section 14 of 36
14. Handle transformations
Logarithms, scaling and other transformations change the analysis scale and interpretation of parameters.
Working checkpoint — statistical variable: Preserve the original variable and transformation formula. Separate planned, exploratory and sensitivity analyses instead of merging their narratives.
For students, ask what the graph shows that the average hides.
Section 15 of 36
15. Handle multiple testing
Testing many hypotheses increases opportunities for extreme results by chance.
Working checkpoint — study design: Define the test family and adjustment method. Pin ontology, code, package and data versions before attempting reproduction.
For parents, the useful checkpoint is whether the child can explain the conclusion in ordinary language.
Section 16 of 36
16. Estimate effect size
The magnitude and direction of an effect often matter more than whether a threshold was crossed.
Working checkpoint — probability distribution: Report the estimate in a domain-readable unit. Keep question, estimand, design, variables, model, software and outputs in one analysis record.
For mathematics, connect formulas to the design assumptions that make them meaningful.
Section 17 of 36
17. Quantify uncertainty
Standard errors, intervals and posterior summaries depend on a model, design and estimation procedure.
Working checkpoint — test statistic: Name the uncertainty measure and its assumptions. Link every assumption check and diagnostic to the exact data and fitted model.
For computing, preserve executable code, dependency versions and machine-readable method identifiers.
Section 18 of 36
18. Record software and parameters
A method label does not capture package, version, formula, optimiser, defaults or reference levels.
Working checkpoint — analysis provenance: Export executable configuration and environment details. Report effect size, uncertainty and limitations alongside any significance measure.
For writing, distinguish observation, estimate, uncertainty and interpretation in separate sentences.
Section 19 of 36
19. Preserve random seeds
Simulation, resampling and stochastic optimisation need controlled randomness for closer reproduction.
Working checkpoint — STATO identifier: Store seed and algorithm with the code. Separate planned, exploratory and sensitivity analyses instead of merging their narratives.
For students, ask what the graph shows that the average hides.
Section 20 of 36
20. Link diagnostics
A diagnostic has meaning only in relation to the exact model fit and dataset.
Working checkpoint — statistical variable: Keep residuals, plots and flags with model identity. Pin ontology, code, package and data versions before attempting reproduction.
For parents, the useful checkpoint is whether the child can explain the conclusion in ordinary language.
Section 21 of 36
21. Separate planned and exploratory work
Exploration is valuable, but it should not be presented as if every choice was specified before seeing data.
Working checkpoint — study design: Label analysis status and amendment history. Keep question, estimand, design, variables, model, software and outputs in one analysis record.
For mathematics, connect formulas to the design assumptions that make them meaningful.
Section 22 of 36
22. Audit data exclusions
Removing observations can change the estimate and uncertainty, especially in small samples.
Working checkpoint — probability distribution: Report rules, counts, reasons and sensitivity results. Link every assumption check and diagnostic to the exact data and fitted model.
For computing, preserve executable code, dependency versions and machine-readable method identifiers.
Section 23 of 36
23. Challenge p-value certainty
A p-value does not state the probability that the hypothesis is true or the importance of the effect.
Working checkpoint — test statistic: Pair it with estimate, interval, design and limitations. Report effect size, uncertainty and limitations alongside any significance measure.
For writing, distinguish observation, estimate, uncertainty and interpretation in separate sentences.
Section 24 of 36
24. Challenge independence
Repeated or clustered observations can make naive standard errors too small.
Working checkpoint — analysis provenance: Model or justify the dependence structure. Separate planned, exploratory and sensitivity analyses instead of merging their narratives.
For students, ask what the graph shows that the average hides.
Section 25 of 36
25. Challenge causal language
Association alone does not establish that changing one variable will change another.
Working checkpoint — STATO identifier: State the design and causal assumptions before using causal verbs. Pin ontology, code, package and data versions before attempting reproduction.
For parents, the useful checkpoint is whether the child can explain the conclusion in ordinary language.
Section 26 of 36
26. Challenge model fit
A converged model can still fit poorly, extrapolate or rely on influential points.
Working checkpoint — statistical variable: Inspect diagnostics and plausible alternatives. Keep question, estimand, design, variables, model, software and outputs in one analysis record.
For mathematics, connect formulas to the design assumptions that make them meaningful.
Section 27 of 36
27. Review ontology and code migration
Updated classes, packages or defaults can alter method representation and results.
Working checkpoint — study design: Run version comparisons before replacing the production analysis. Link every assumption check and diagnostic to the exact data and fitted model.
For computing, preserve executable code, dependency versions and machine-readable method identifiers.
Section 28 of 36
28. Connect to Primary Science
Simple class surveys and repeated measurements show why individual observations matter beside an average.
Working checkpoint — probability distribution: Use small visible datasets and hand-drawn plots. Report effect size, uncertainty and limitations alongside any significance measure.
For writing, distinguish observation, estimate, uncertainty and interpretation in separate sentences.
Section 29 of 36
29. Connect to Secondary Science
Experimental design, variables, uncertainty and graph choice support evidence-based conclusions.
Working checkpoint — test statistic: Ask what alternative explanation the design cannot rule out. Separate planned, exploratory and sensitivity analyses instead of merging their narratives.
For students, ask what the graph shows that the average hides.
Section 30 of 36
30. Connect to mathematics
Probability, distributions, estimation and algebra make statistical models understandable rather than button-driven.
Working checkpoint — analysis provenance: Work one small calculation and interpret every symbol. Pin ontology, code, package and data versions before attempting reproduction.
For parents, the useful checkpoint is whether the child can explain the conclusion in ordinary language.
Section 31 of 36
31. Connect to computing
Data schemas, scripts, tests and environment capture turn an analysis into a reproducible workflow.
Working checkpoint — STATO identifier: Automate checks for roles, ranges, missingness and versions. Keep question, estimand, design, variables, model, software and outputs in one analysis record.
For mathematics, connect formulas to the design assumptions that make them meaningful.
Section 32 of 36
32. Connect to pathways
Statistical semantics matters in research, public health, engineering, data science, economics and policy evaluation.
Working checkpoint — statistical variable: Check current official course and career information separately. Link every assumption check and diagnostic to the exact data and fitted model.
For computing, preserve executable code, dependency versions and machine-readable method identifiers.
Section 33 of 36
33. Did you know?
The official STATO page includes plots and graphical representations in scope, recognising that visual checks are part of statistical review.
Working checkpoint — study design: Pair one numerical summary with a plot and compare what each reveals. Report effect size, uncertainty and limitations alongside any significance measure.
For writing, distinguish observation, estimate, uncertainty and interpretation in separate sentences.
Section 34 of 36
34. Write a reader-ready analysis note
Name the question, population, design, variables, method, assumptions, software, estimate, uncertainty and limitations.
Working checkpoint — probability distribution: Let another reader reconstruct the logic without guessing. Separate planned, exploratory and sensitivity analyses instead of merging their narratives.
For students, ask what the graph shows that the average hides.
Section 35 of 36
35. Build a validation ladder
Check data identity, design, units, variables, assumptions, code, diagnostics, estimates, uncertainty and interpretation.
Working checkpoint — test statistic: Stop confidence at the earliest failed rung. Pin ontology, code, package and data versions before attempting reproduction.
For parents, the useful checkpoint is whether the child can explain the conclusion in ordinary language.
Section 36 of 36
36. Finish with a reproducible analysis bundle
Deliver frozen data, dictionaries, plans, code, environment, ontology release, outputs, diagnostics and narrative limitations.
Working checkpoint — analysis provenance: Make every result traceable to observations and choices. Keep question, estimand, design, variables, model, software and outputs in one analysis record.
For mathematics, connect formulas to the design assumptions that make them meaningful.
Contents · Previous section · Continue to the Science Learning Hub